Questions about Warrior Cooldowns

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1) Which bosses have damage spikes I need to save Inner Beast for?
All the extremes, and all coils T5 onwards. On anything else it doesn't mean so much. Additionally, on Leviathan extreme the nuke is so far apart you can happily use Inner Beast when it's up, and save nothing. In Moogle Ex it's much harder to predict, also, so these two extremes are a bit of an exception.

2) How should I use my cooldowns on bosses without spikes?
Save them for when the healer doesn't heal (so when you're low hp).

3) In what situations should I be using Berserk and Unchained?
When you pull, it's usually best to go Infuriate > Tomahawk > Brutal Swing > Heavy Swing > Unchained > Skull Sunder > Berserk > Butcher's Block, for some very high initial aggro, so you don't lose it to anyone at the start. Also, you absolutely should not be using cooldowns, except Infuriate, prior to pulling like the guy above me says, as you will waste precious seconds of them. Always aggro before using cooldowns, except for Infuriate because it can be treated as consumable, and not a duration-based cooldown.
Additionally, unchained isn't very commonly used, in that it's usually better to just use Inner Beast for its defensive purpose, or Steel Cyclone to AoE, but you could use it any time you pleased when you're not saving wrath stacks to Inner Beast before a specific nuke. The same goes for Berserk; use it as you please unless you're gonna need to Inner Beast a specific attack, in case you get Pacified and can't use Inner Beast.

4) For weaker cooldowns like Foresight and Bloodbath, should I macro these to other skills, like Heavy Swing, in order to maximize their uptime?
Personally, I don't use macros, but you could for these if you wish. That said, it's common in fights for you to not have a cooldown for a big nuke- you cannot always have cooldowns up for Twintania's Death Sentence (excluding Inner Beast), for example, so typically all these weaker cooldowns- foresight, bloodbath, awareness, convalescence, featherfoot, to name most of them- are used together to work as a pseudo-cooldown. If you're not planning on doing that, and instead plan on taking a naked nuke, sure, macro them to skills. These skills are pretty damn weak and so it doesn't really matter when you use them, so much.

5) Should I macro skills that synergize well with each other, like Thrill of Battle and Convalescence, together?
Read the above. Also, what on earth makes you think Thrill of Battle and Convalescence go together at all? I mean, with increased max hp, both Lustrate and Stoneskin are going to be healing you for much more, and both ignore the effects of Convalescence. Honestly, of any two cooldowns, I'd say these two work together the LEAST well.

6) How should I be using Infuriate, and Wrath stacks in general?
As said in 3), you can be using Unchained as you please, however you may prefer to spend wrath stacks on Inner Beast because of the defensive gain it gives you for a little while. Additionally, so you do not waste wrath stacks (as the increased crit rate is nigh worthless), you should be using one of the three skills whenever you have enough stacks to do so, except for when saving them for use of Inner Beast on a nuke, or Steel Cyclone for an AoE. On a related note, unless you know a big nuke is coming up soon (to Inner Beast for it), you should be using Infuriate whenever it's up and you have 1 or no stacks.

7) Which cooldowns, if any, should I be using against trash packs?
Bloodbath and Vengeance on very large pulls, possibly Holmgang too, when speedrunning. That's all.

Hope I helped, and I'd love to see what other people put as a response.