Tableegh and Taleem

Q: I grew up in a home where my dad always went out in Jamaat and did Taleem at home. I am married to a Muslim man who is kind and generous Alhamdullilah but does not believe in tableegh work, he refuses to go out even for 3 days. I have made dua many times but he refused. He will sit and listen when Jamaat visits our home but his dad told him not to go with the "tabhleegis" if I can put it like that. Please elloborate to me in simple terms

1. What is Tableegh and why the Jamaat goes out doing Tableegh work so I can explain to him and his family. Alot of them also say that Taleem is a tabhleegis practice and that's the reason they don't do it.

2. Also they believe in reading Salaami which I was never taught. One question also raised is that why don't we read the salaami in the Taleem groups done by women weekly? 

Meaning of amr bil maroof and inviting towards Islam

Q: I would like to inquire regarding the following:

1. Does the amr bil maroof abundantly mentioned in the Qur'an include inviting non Muslims towards Islam?

2. Which should be given preference/which is more important, inviting non Muslims towards Islam, or inviting Muslims to uphold the deen completely? Does one hold greater importance over the other or are both equal in importance?

3. If one carries out one out of the two above, will it be considered to be deficient for not carrying out the other?

Woman refusing marriage proposals because she feels she is not 'mentally ready'

Q: Can a Muslim woman of marriageable age refuse marriage proposals altogether from Muslim men of good deen and character without meeting them with the approval of her father who is seeking a good spouse for his daughter, or accepts to meet with them due to her father putting pressure on her to get married with the intention of refusing the proposal before meeting the male prospective and then following through to decline the proposal after meeting them because she feels she is not 'mentally ready' for the responsibilities of marriage, or she says that there aren't any 'good' boys left due to trauma surrounding the idea of marriage, after witnessing firsthand from a young age her elder brothers 3 very toxic, unislamic and abusive marriages that all ended in divorce?

According to Islam, are there any valid reasons for a female choosing not to get married or to get married at a later stage (when one is mentally ready etc.)

And if a female is to choose not to marry, how is she expected to live her life whilst under the care of her elderly parents? Is she expected to stay at home or can she go out and work to take care of herself etc.?

And what category (fardh, waajib, musthab, sunnah etc.) does marriage fall under and what category does choosing not to marry for the above reasons fall under for a Muslim female? And what category would refusing a good proposal fall under? (Makrooh, haraam etc.)

Also, what is the responsibility of the parents and especially the father in the above scenario? Is it correct for him to keep pressuring his daughter to accept proposals coming home before making a decision for marriage (Note: he isn't forcing her to get married to anyone specific but is encouraging her to get married and leaving the final decision to his daughter after bringing good proposals for her given her age and that he is elderly and concerned for her wellbeing should anything happen to him) or should he decline the marriage proposals until his daughter is ready despite his concerns for her future?

What advice would you give to the father and daughter in the above situation?