Sandon

Welcome to the NGC chat board.
   I assume that by "conditioned" you mean "conserved". NCS (NGC's affiliate) uses processes that can remove surface contaminants from coins but cannot remove or reverse corrosion, nor could the deep cuts be repaired. See Coin Conservation | NCS | Numismatic Conservation Services | NGC (ngccoin.com).  
   You may want to try soaking this New Jersey copper in acetone or even distilled water to see if this improves its appearance by removing any mud or other residue that hasn't chemically become part of the coin's surface.  The coin could only be "Details" graded even if successfully "conserved" and, in my opinion, wouldn't be worth the substantial cost of conservation, grading and shipping. See NGC Services and Fees | NGC (ngccoin.com).  If you do decide to submit it, it may be somewhat less expensive to do so through an NGC member dealer instead of submitting it yourself. See Find Coin Shops & Dealers | Coin Dealer Locator | NGC (ngccoin.com).
   This piece is still rather nice for a "ground find". 
   
   

Proof 1964 Washington quarter, NGC graded PF 69 though not as mirrorlike as some and rather inexpensive:

1880 Proof Liberty Seated half dollar, NGC graded PF 62 (older holder):

1880 Proof Liberty Seated half dollar, NGC graded PF 62 (older holder):

1877 Shield nickel (proof-only key date), PCGS graded PR 63:

 

1903-O Morgan dollar, PCGS graded MS 64:

1905 Liberty nickel, PCGS graded MS 64:


Photos courtesy of Stacks Bowers Galleries.

1872 gold dollar (mintage 3,500), recently NGC graded MS 60:

1888 proof copper nickel three cent piece in old green label PCGS holder as PR 65:
 

1899 Liberty double eagle, now NGC graded AU 55:

Proof 1964 Washington quarter, NGC graded PF 69 though not as mirrorlike as some and rather inexpensive:

1880 Proof Liberty Seated half dollar, NGC graded PF 62 (older holder):

1877 Shield nickel (proof-only key date), PCGS graded PR 63:

 

1882 Shield nickel, PCGS graded MS 64:


Photos courtesy of Stacks Bowers Galleries.

This coin is likely counterfeit, though apparently modeled from a genuine O-102. The odd surface texture and uneven wear are suspicious.
    What does the edge of the coin look like?  A 1795 half dollar should have "FIFTY CENTS OR HALF A DOLLAR" with decorations between the words as shown on this image from NGC VarietyPlus:
    

The only price guide available to me that lists this coin in this exact grade is the PCGS Price Guide, which gives a current retail value of $260 for an 1880-S Morgan dollar graded MS 64+ PL. https://www.pcgs.com/prices/detail/morgan-dollar/744/grades-61-70/ms.  The NGC Price Guide lists an 1880-S Morgan dollar in MS 64 PL at $190 and in MS 65 PL at $275 (value last updated October 2020).  Morgan Dollars (1878-1921) | Price Guide & Values | NGC (ngccoin.com). The current (April-June) CPG Rare Coin Market Review has MS 64 PL at $257 and MS 65 PL at $358. The green CAC sticker indicates that the coin is "solid for the grade" whether NGC or PCGS graded it in the opinion of the CAC graders, so the $260 usually high PCGS value is probably a good estimate. 
   If you want to look for actual sale prices for CAC approved coins in this grade, you would likely do better to check the auction archives on the sites of major numismatic auctioneers, such as Great Collections, Heritage (ha.com), and Stacks Bowers. In my opinion, reported sales on eBay may be questionable.
   

In addition to awaiting any additional responses on this forum, you might want to post this coin on the CONECA forum at https://board.conecaonline.org/forum. You can also request an opinion from Jon Sullivan, a respected errors dealer, at https://sullivannumismatics.com/contact-us/.  If this coin were authenticated as a genuine indent strike or other significant mint error, it would have some value, although, as each error coin is unique, how much is difficult to say. I continue to have my own misgivings as to its authenticity.

1877 Shield nickel (proof-only key date), PCGS graded PR 63:

 

1951 Lincoln cent, PCGS graded MS 66 RD:

Welcome to the forum, that is a very nice introduction.  As to your questions:
1) I have used acetone on almost every US coin with no issue, I do not collect world coins so I cannot provide any information on if there are any issues bathing any world coins in acetone or not.   It is best not to soak any coins in acetone for extended times unless the coin has a significant amount of PVC or gunk on it, a simple swish around in the acetone or a 10 min bath is enough to remove most surface contaminates.
2) Glass is best with a lid for a longer soak, acetone evaporates very quickly.
3) Not usually but it depends on the origin of the toning, remember that toning is the interference of light reflecting off the surface of the coin, if what you remove affects that effect then you could see some change.   Best to try this with your least favorite toned coin first.
4) While I suspect you can I don't usually myself, I use plastic coin tongs to hold the coin and simple swish the coin around in the acetone for 10 seconds or so, again only soaking if there is a substantial buildup of something.   And usually, I use two containers of acetone, one for the first rinse than a second to make sure that any surface contaminates did not redeposit onto the coin from the first rinse.   And it is important to change the acetone often if you are doing several coins to avoid having something from one coin redeposit onto another from the dirty acetone.
I do not consider the use of acetone as cleaning, but there are collectors and dealers who frown on its use.

Welcome to the NGC chat board. The "Coin Marketplace" forum is dedicated to topics offering to buy or sell coins in accordance with the Guidelines posted near the top of the forum, with which your topic does not comply.  A topic like this one should be posted on the "Newbie Coin Collecting Questions" forum, where it would receive appropriate attention. You should not offer to sell a coin when you have no knowledge of its value.
    The images you provided of your 1998-D cent are too brightly lit and/or have inadequate resolution to see any details clearly, as well as being uncropped.  Try to post clearer images that are cropped like this:
  
 
  I think I see some light, shallow "strike doubling", also known as machine or mechanical doubling north of "WE TRUST", which is extremely common and of no collector value. See Double Dies vs. Machine Doubling | NGC (ngccoin.com).  I can see no mint-made anomaly on the "A" in "AMERICA", which may have suffered a nick. 
   You appear to be a victim of internet disinformation. In reality, it is extremely unusual to find any coin of substantial value in pocket change. Submitting coins for third-party grading is for those who have sufficient knowledge and experience to make a likely determination of the coin's identity, grade and value. 

Your best defense against counterfeits is understanding what the genuine pieces are supposed to look like. Most of the counterfeits we see here are detectable on sight due to their differences in design details and overall appearance from genuine coins.  Even most of the more deceptive ones can be identified by understanding the characteristics of particular types of counterfeits. See, for example, NGC Counterfeit Detection | Identify Counterfeit Coins | NGC (ngccoin.com).
   Although an accurate scale and compositional tests may also be of value in detecting some counterfeits, they are no substitute for knowledge of and experience with the coins that you collect. I also recommend that if you do not have such knowledge, you do not buy uncertified coins--or perhaps any coins of significant value--on sites such as eBay, except from well-known, reputable dealers such as those who are members of the Professional Numismatists Guild (PNG). See https://www.pngdealers.org/af_memberdirectory.asp.

Yes, it is a "type 2" "S" mint mark as that term is used on 1979 proof coinage. The determination is made by the shape of the mint mark.

Not a DDO, just some worthless strike doubling.   This happens when the  die is loose in the press, and it happens quite often hence the no added value.

1882 Shield nickel, PCGS graded MS 64:


Photos courtesy of Stacks Bowers Galleries.