If you are thrown in at the deep end, you have to deal with serious issues the moment you start something like a job, instead of having time to acquire experience.
To make an angry protest against a relatively minor problem, in the process embarrassing the protester. The analogy is with a baby who throws toys out of the pram in order to get their parent to pay attention to them. The implication in the idiom is that the protester is acting like a baby.
To meet or fit the criteria or expectations. For example, "This product ticked all the right boxes for me", or "That applicant's interview didn't go so well; it didn't tick any of my boxes".
Small changes may have little effect until they build up to critical mass, then the next small change may suddenly change everything. this is the tipping point.
If something is to little avail, it means that, despite great efforts, something ended in failure, but taking comfort from the knowledge that nothing else could have been done to avert or avoid the result.
This means juggling too many projects at once and something's bound to fail; when a smith had too many irons in his fire, he couldn't effectively keep track of all of them.