I've heard that a ball can hook out or roll out when it is too strong for the condition. How can you tell the difference between this and carrydown or a longer or heavier pattern?

When I've noticed it, it's normally been when a ball makes its move to the pocket and it hits, it deflects instead of continuing through the pins. Quite often when the ball is deflecting as so, you'll be leaving soft/flat 7 or 10 pins depending on what hand you use.

It's an adjustment you just need to know.  It definitely looks like carry down, but if you are lined up and make an adjustment you think is for carry down you are now going to be 2 adjustments behind.  Always make the move in and you will be correct 99.9% of the time.

if it's in practice or the first half of the first game you may need to square up for some carry down, but after that move in or you are just giving frames away.

Obviously this is just about bowling on one pair of lanes.  If you are crossing pairs in a tournament you may need to move on different pairs as some pairs will play tighter than others.

But if there is a guy bowling inside of me, swinging into my line, and my ball starts going longer/losing reaction - is this carry down?  What is the adjustment for this situation?

10 years ago maybe it was carry down.  Still true carry down is only seen at the break point (40 or so feet down lane) where you see the ball "wiggle" when it should be making it's move to the pocket.  In you situation I'd still be willing to bet that you used up most of the head oil where you're playing and you need to move further in.  If you're accurate in the heads, and you have an aggressive ball (either a high end ball or anything with a decent amount of surface) you can very much deplete your own head oil in about half a game.  Yes, it's never fun to have to move in where some one else is already playing because the heads might already be beat up there.  Even it you move in a little deeper than the other bowler, trust the move.  If you've already worn a spot in the lane even guys without a ton of hand can move in pretty deep.  Your break point won't really change, just the initial angle of how you get there.

A good example was this past Tuesday.  I was bowling on Scorpion (47 feet, 26.1 mL of oil) which plays inside and pretty slick.  I was using a Loaded Revolver at 2000 grit hitting 12/13 at the arrows out to about 9 at the break point.  After about a game my line just didn't look as good.  I lost the tug room that I had and anything a hair wide just wouldn't make it back to the pocket.  After thinking I had little to lose I moved in 4 and 2.  My line instantly looked 100% better.  Unfortunately I wasted 4 frames thinking I just wasn't executing my shots.  Even people who should know better sometimes don't make the correct move or move soon enough.  Basically, it your line no longer looks good, make a move.  The worst thing that can happen is that it's no better than where you already weren't having any luck.

When moving 3-4 deeper, that feet or target or both?

I've never figured this one out myself.

On 1 or 2 boards I might not move my eyes, but for bigger moves you also want to move your target in some also.  If you only move your feet and move in 4-5 boards you'll throw it through your break point.  A general rule is to move your eyes 1/2 of how far you move your feet.  2 and 1 or 4 and 2.  How much you move either is sometimes dictated by whether you're trying to take advantage of hold or hook.  If you're trying to use the hold it's more likely to be 4/2 or 4/3.  If you're trying to hooking the ball a lot it's more likely to be 2/0 or 3/1.