[BillyCoxDodgers3B]

Your first question presents quite the conundrum. I could never give a blanket answer on it; each instance would have to be weighed on its own, as you just never know which you might prefer until faced with the two cards in question. I would think, however, that I'd usually pass on a trimmed card if an untrimmed was available. Same goes for a taped over autograph on a card, and most often for something with extreme paper loss/non-removable scrapbook residue on the back. For that last example, however, I may still opt for that card if it has a beautiful autograph, the front displays fetchingly and the corners still look amazing thanks to being placed in a scrapbook vs. something soiled, rounded corners, O/C, etc. It's all on a case by case basis.

One related thing I want to add which you didn't mention, yet is important: if presented with two of the same card, I have to sometimes try to put my personal likes/dislikes aside and consider which of the two cards would end up having the broadest appeal to the next prospective buyer. I've faced that situation more than once, and it can sometimes be a challenging decision between the example I like the most vs. the one that I know others would better appreciate! Normally, I tend to fall on the same side as what I figure the general collecting population would opt for, but there have been instances of the opposite! If people aren't collecting with any thought towards later resale, then the decision becomes vastly easier!

Yet another related answer to a question you didn't ask (ha!): say I'm presented with two cards in fairly similar condition. One has an ink signature which for whatever reason is not ideal. The other has a bold pencil or pencil crayon autograph. I'm probably going to opt for the latter! These situations almost exclusively happen with pre-War cards, so chances are it's a case of a long-deceased player. If it's a player who lived to an advanced age, well into when the hobby grew, then I would just pass altogether and wait for something better to come along.

As to your last question, by all means, YES!

Here's an interesting example of two that I own. Joe Moore was a wonderful human being and was also my friend. First off, forget about the PSA slab on the one card and just pretend both are slabbed, or raw. If presented with both of these, which to keep and which to divest? The one features a career era, green fountain pen autograph, but is a touch lighter than the next example. The other has a bold, blue ballpoint signature, but signed post-career. It was definitely signed when Joe was still healthy and his signature hadn't started exhibiting the signs of aging. In this case, I'm sticking with the fountain pen. It's obviously also signed in the optimal spot. (It's more of a no-brainer decision based solely on these scans. If you had them in hand, you'd understand why the decision would become harder. The ballpoint is darker in person than the scan would suggest; the fountain pen lighter.)