Search Results: ask her to be my girlfriend

Been dating a female for about 6 months… We went on 1 date & spent quality time with each other twice… I was approached by this female saying she liked me and wanted me for years once she found out i was no longer in a relationship… We texted everyday… The chemistry, charisma, & sexual tension was definitely there… She told me she was single when i asked about her ex fiancé who she was engaged to… she said for a year & 43 days which I’m assuming it was due to him being incarcerated… he is the father of 2 of her kids… She said they still had love for one another but they decided they were better off as best friends… when she got overwhelmed & overstimulated with personal issues she would push me away & shut me out for days at a time… Her distancing herself started to bother me so i communicated it to her which she said if we communicated things would work out between us so that’s what i did… she became angry at me… she said how she eventually wanted to be my girlfriend and had future plans with me in them… she said she could see herself falling in love with me because im a good person but then we had a disagreement because the distancing became more common than ever… so she said i was suffocating her because i didn’t believe anything she told me so we friend zoned one another… Then she kept texting me i told her to stop texting me… she texted me one day saying she missed me… So we were back in good graces… Then i planned something special for her because i knew she was going through some personal issues and i had Christmas gifts for her… So on Saturday we had sex after she seen her romantic gesture and gifts but that same day she said her baby father was coming home soon… she texted me Sunday thanking me for the best few hours she had in a long time & she kept admiring her flowers while smiling so hard… Then after that things got weird she only texts me in the mornings now… my assumption is he’s home…

I want to get feedback on my partner:

- She’s not keen on me seeing friends, for my safety and would rather I met them with her. She also uses the find my iPhone feature with me.
- She messages me and phones various times per day, and gets frustrated if I don’t reply quickly, she says it’s to check I’m ok,
- She tracks my spending on her, to check we’re in budget. Even if I a buy a coffee she’s brings it up and asks why I bought it.
- She’s says if I don’t spend $$ on her birthday present I don’t love her. Also said her birthday needs to be “perfect” with hundreds of balloons etc and fancy cake.
- She doesn’t like me having a female friend at work, has told me to stop going to lunch with her. Said it’s to ensure I don’t “cheat”. She messaged my friend at work on Facebook to ask about me.
- My partner doesn’t like me following other girls on social media even friends.
- She told me I can’t have anyone better than her.

Is she a good partner? I’m really conflicted as this is my first relationship. My female friend said there is red flags everywhere, is she right?