Part-time educator job not including deductions in paystub, plans to file 1099 form later.

To give some context, in March of this year, I was offered a full-time internship where, upon completion of 250 hours at a general rate of about 32 hours/week, I would be paid a $1,200 stipend. At the time, I was given a W-4 form where, under the multiple jobs section, as I was unsure on how to classify my internship at the time, and I was also doing (and still do) a part-time childcare job for a home and community-based service provider, I checked the option for "only two jobs total." 

Once my internship was over, I was offered a position as a part-time education assistant, where my scheduled hours were determined in consultation with my director. This meant that my hours were variable, as rather than coming in to work on set days for a certain number of hours, I was on-the-call for when my director needed me to fill a shift. I was paid at a rate of $12/hour in this new position, though as of my most recent paystub, I was actually supposed to be paid $14.50/hour, and I received backpay to compensate for the missing partial wages. 

I've noticed that in all of my paystubs, no deductions are taken, including federal income tax, state (MD) income tax, social security, and Medicare. I found that peculiar, but according to a note on the paystubs, my company plans on filing a 1099 form at some point. From what I researched, 1099 forms report payments typically not from an employer, and I believe that fits with my $1,200 internship stipend, either as a 1099-NEC ($600 or more in nonemployee compensation) or 1099-MISC (ex. prizes and awards). Even so, I fail to understand how a 1099 form applies to my current situation as a part-time education assistant, even if I have variable hours. I read that 1099 forms are typically for independent contractors, but that does not fit my situation, as we actually have a person who comes to our workplace that can be considered a contractor, given that he arrives afterhours and works on his own, whereas I am given direct orders from my boss on what I should do. Is it usual for my work to file a 1099 form for both my internship and part-time job, or should I also ask for a W-2 form to cover the latter? 

In addition, as I need to make some updates to my W-4 forms, notably that I currently have more than two jobs, for this specific job that I mentioned in the post, when making note of the wages, should I include the $1,200 stipend or just focus on the hourly wages?

Thank you in advance.