I'm not going to try and tell you the best use since I'm no DRK expert, but when tanking if you want to get the most out of your buffs, one of the most important factors is the CD times of each of your skills. For example, if you're saving a buff with a 90s CD so that you'll have it in >3 minutes, you just halved the amount of time it could have been mitigating damage for you.

Now taking CD times into consideration, simply cycling them from shortest CD time to longest (saving big buffs as needed) you'll be able to maximize the amount of time you spend buffed. As for Foresight, it's not great, but as your healer I'd be more appreciative of consistent buffing, rather than bursts of heavier buffing when it comes to trash because trash is consistent repetitive damage, and so you can make yourself more consistently manageable. Worry less about buffing as mobs start dying off and instead you can focus on reserving them for later, because your incoming damage has now decreased and you're less difficult to keep alive.

Like I said I'm not a DRK expert, you're not a pld and don't have as many CDs to cycle, so you'll want to take more advantage of breaks in damage, such as a WHM using Holy which stuns the mobs, etc. if you're able. And you may want to allow for breaks in between your buffs just to allow for more time spent on skills cooling down.

As for the healers part in this; that feeling of your HP rising and plummeting sometimes and not others is probably because your healer isn't utilizing their shields or Regens. On trash an AST is best off being in Diurnal stance, which allows him to keep up a regen on you, stabilizing your hp a bit and making up the difference with small or large heals as needed, and WHM does the same thing. SCH is a little more complicated and it has a variety of options, but it has a couple shields meaning you take less damage, and also has Eos and themselves healing you in rotation which can feel similar to a regen. There's also the odd thing like the ability to AoE stun--and then some healers DPS and others don't. And lastly if other things are going on, like DPS are taking damage, that takes away from a healer healing you.

Maximizing up-time is important on trash, but on trials and raids it's important to prioritize managing burst damage first and then you can think about popping buffs in between to make the overall experience smoother. Hopefully an experienced DRK will be able to post here with more specifics on how to mitigate AS a DRK, but ultimately the key is understanding healer strain (where the damage is coming from, how much and how consistent)