Is gaining 130 mmr over a month and a half acceptable for improvement or is that slow?

any improvement can be good, even as small as that you are still making progress.

depends on your standards. ^^ My mmr hasn't changed since I started playing ranked, like 5-6 months ago.

I have since climbed from bronze 5 and today am almost in my second promos to bronze 3...

Depends how much you played during that time.