[RPG] What can players do while waiting for a troll to regenerate

This has been addressed in the PHB errata:

Suffocating (p. 183). If you run out of breath or are choking, you can’t regain hit points or be stabilized until you can breathe again.

There's loads of drawbacks to time limits on turns.

A few have already been mentioned by other answers; I include them here for the sake of completeness, with details from my own experiences:

• Time limits on turns penalize players for having mechanically complex characters with a lot of options. Given that Pathfinder is a system that generally rewards players for building complex characters with a lot of options, this might annoy players who like that sort of playstyle. I've heard of people trying to counter this by giving players of analysis paralysis-prone classes (such as wizards) extra time, but any system that gives players varying turn time limits is going to require discussion before you get player buy-in.
• Time limits on turns raise questions about what does and doesn't count toward a player's turn. If a player decides what to do while they still have time, but resolving the action pushes them over the limit, do they get to finish? What if the only reason they went over the time limit was because something they did provoked an attack of opportunity from a character whose attacks of opportunity take forever to resolve? What if one of the player's dice falls into their drink, and has to be wiped dry before it can be used? What if the player receives an urgent phone call? What if a different player receives an urgent phone call, and insists on everyone else waiting for it to end? What if the player makes their decision in a timely fashion, but during their move action moves into a position where they can see something new, and the GM has to describe it? What if the player learns information during their move action that renders their plan for their standard action unfeasible, forcing them to re-evaluate? If all the turn just prior to the player's changed the battlefield drastically, is it fair for them to get a little more time? A group can answer any and all of these questions, of course, but they're not all clear-cut and easy questions to answer, and disagreements over what the answer should be can detract from play.
• Time limits on turns tie character skill to player skill, which limits what kind of characters players are able to roleplay. In effect, players who are less familiar with the rules or less skilled at making quick decisions are prohibited from playing characters who are quick, decisive, and highly intelligent. One of the pleasures of RPGs is the potential to play a character with strengths you don't have, and time limits can undermine that.
• Time limits on turns discourage players from asking questions about their surroundings and making clever plans. In-character, a lot of details about the environment should be obvious at a glance. Players, on the other hand, have to ask for this information and wait for the GM to explain it, which takes time: "Is the chandelier held up by ropes or chains? How many? And how far off the floor is it?" Yes, you can rule that time spent on such queries doesn't count towards a player's turn, but the time a player requires to translate received information into their mental model of the in-play environment and formulate follow-up questions is harder to account for. In addition, the complex tactics and creative plans that can be built on such information take time to come up with - and since such plans are a big part of the enjoyment of the game for some players, discouraging them can be a bit of a downer.

And here's some previously-unmentioned drawbacks to time limits on turns from my own experience as a GM and player:

• Having time limits on turns may make players feel condescended to. I've known players to interpret an imposed time limit as a suggestion that they couldn't manage their time otherwise, which they found insulting. To be fair, saying you'll count to some specific number and not let someone play if they don't stop misbehaving is treating someone like a child. There's ways of presenting the idea that help avoid hurt feelings, but some players will feel insulted no matter how you try soften the blow.
• Having time limits on turns can make players feel rushed. Yes, that's the whole point, but bear in mind that some players find being rushed stressful, and prefer a more relaxed pace of play. Potentially you could offset this by removing other sources of stress, though you'll have to consider what your players find stressful to do that.
• Time limits on turns increase the amount of bookkeeping required by the game. Not by much, admittedly, but having to pay attention to a stopwatch or a collection of hourglasses is an additional cognitive weight added to a system already heavy with bookkeeping complexity. Worse, the brunt of this mental load is borne by the Game Master, who already has a lot to deal with without having to stare distractedly at a sand-glass.
• Time limits on turns may lead players to make mistakes in their haste, leading them to frustration. A too-hasty judgement can be the difference between life and death, or between flesh and stone, or between having one's soul stolen and getting to keep it, and realising that you would have been able to avoid an undesirable outcome if you'd had another minute or two to contemplate can be incredibly frustrating. You can reduce the frequency of this by having longer time limits, but it will almost certainly still happen occasionally if your time limits are short enough to provide their intended benefit.
• Assuming that the penalty for not finishing one's turn within the time limit is losing one's actions for the round, time limits on turns may prevent a player from roleplaying competent characters. This is similar to the already-mentioned drawback of time limits also limiting roleplaying options, but is even worse: Some players may find themselves effectively forced to play characters who are apparently incompetent in combat. This is doubly-true if they built a mechanically complex character before the time limit was imposed.
• Time limits on turns discourage players from acting in-character during combat. Many players find banter and conversation and acting out character dialogue and describing their characters' actions fun things to do both in-combat and out, but time limits on turns rather limit the benefit of talking being a free action. (This is true even without your imposed rule about players not being able to speak on each others' turns - though, not being able to speak on each others' turns will make it much worse, and will give players even less reason to engage with the game when it's not their turn.)

The actual impact of the above drawbacks is playstyle-dependent. Personally, I find them too irksome to bother with, but I've known tables that barely noticed most of them, or were willing to live with the drawbacks of turn time limits as long as they continued to be outweighed by the benefits. I've therefore mentioned every method of mitigating those drawbacks that I know of, with one big exception: Nearly every drawback I've mentioned above can be mitigated to some extent by increasing the time players have to complete their turns in. Of course, this also reduces the benefit of having turn time limits in the first place.

If my answer has discouraged you from using turn time limits (and it should have), a good alternative is to tell your players that you would like to keep combat snappy and exciting, and suggest they pay attention during each others' turns so that they can plan their actions in advance. (This is easier if you allow players to speak when it's not their turn, so that they can participate in combat banter.) Provided that your players are responsible and self-disciplined adults, they'll most likely agree with your reasoning and co-operate. In my experience, this method provides all the benefits of turn time limits listed in your question, without any of the disadvantages listed in this answer.