Application Timing for a starting graduate student

Hi y'all guys!

I'm a European undergrad that Will be starting soon his 1 year MSc. in finance.
I was looking for some summer internships, or graduate programs offers for when I'll be a fresh graduate.
With much surprise I found out the deadlines for the 2019 programs are closing quite soon( i.e. December/January).
Isn't that absurd? I mean on what basis I'm selected or not given the fact that by the deadline I would have probably done any exam yet? On my bachelor Gpa? On what?

Then it comes another couple of questions...
For health and family reason I'm a 21yo with no experience (a part a 2mo stage in a no profit association studying migrations) , is it THAT bad?
Can I apply for SA positions even though I'm not an undergrad or is it better to apply for grad programs and explain this?
Am I f****d up?
Is it better to wait and use the OCR at my uni?

(I'm quite shocked because I thought about applying and looking for jobs around December/January... I was browsing the careers sites just out of curiosity and found out it's better if i move up.)

Thanks