How to continually email references without annoying them? I am beginning to realize that I may need to suddenly bombard my referees with several emails. They have both confirmed that they would be references.

Firstly, I would like to know whether the school I’m applying to has sent them the form yet that they need to fill out. They should have, but I’m not sure if they did. The application is due January 31st. 

Secondly, I sent one of my referees a document of the tasks I worked on during my undergraduate research project to help with the reference. I had a meeting with him last week and he asked me to send this to him. I did yesterday morning and still haven’t heard back. He usually replies very quickly. Should I confirm he received it?

Thirdly, The internal scholarship just opened up and I just found out I need a couple of references for this (it’s only one application). This reference form is nearly identical to one of the other ones I asked them to fill out. I would like to ask them for this reference as well (it’s due at the very beginning of March).

Lastly, assuming they don’t send in their references until right up until the deadline, I will also need to eventually send them a follow up email to make sure they send them in.

I feel like a huge burden emailing them as they are extremely busy (they work with the government in addition to being a professor). How should I go about sending these emails?
People who have agreed to be your referees know you will be applying to various things (or should do: you should have given them a reasonable outline of your plans). The number of different things they need to do is not so important. What matters is the total time it will take them. If they have three references to write at once, they can copy/paste it across, having got into 'writing your reference' mode just once. If you time requests such that they have to keep coming back to it, that will take much more time and effort for them.

So, do your best to group any reference requests into as few blocks as possible. That means you need to plan ahead about your applications, and ask for some well ahead of time, so they can be done along with references for places with earlier deadlines. As a bonus, this also massively reduces the 'night before the deadline' worry.

Personally I would scrub round the 'did you send it?' email. If it's after the deadline, there's not a lot you can do about it either way. If the place you are applying is very strict on the deadline (ie including references), make sure you have told your referees that. Unless you know they are particularly unreliable (in which case you probably want to take a different approach anyway), they will not mess things up for you except in an emergency. Some places will accept references slightly after the deadline, and the nicer ones would let you know that not all your references have arrived, so you can give the referees a poke. Also, if you've given them things in a neat block, there's a good chance they will let you know they've sent the references by themselves.