What I am going to post here is my opinion as I don't mow my true slopes since they are in the 45 degree range. I let my cattle mow those.
Start with mowing your slopes by backing up them. If you can back up it in 2WD you're pretty safe (no reference to side mowing here). If you have to engage 4WD to back up the slope, then in my opinion, care should be taken any time you're mowing it. As others have said; if you have a ROPS, wear a seatbelt. If not, then then no seatbelt. If you need 4WD to back up the slope, get a ROPS before mowing that area.
As for side mowing, trust your gut instincts. If you're not comfortable with it, don't do it. There is nothing wrong with mowing up and down a slope whch "can" be mowed sideways. In all things, safety first.
We all would rather have you around here laughing and joking about backing up a 2 degree slope than to have you have an accident and be injured because of taking an un-needed risk.
As for getting a slope indicator, nothing wrong with it. The numbers may not mean much in the beginning, but as time goes on and you become more comfortable with your tractor the numbers will begin to have relevence.