Is keeping of a beard compulsory for men?

Q: My cousin wanted to know that keeping beard is compulsory for muslim men? Is there no excuse of not keeping it? If his wife does not want him to keep and she doesn't feel attracted towards her husband in beard then is it permissible to not grow beard. Because there are excuses for men if he doesn't feel attracted towards his wife in joint heavy big eyebrows then she can trim it for the sake of her husband. But why the same rule doesn't applies to a lady? Kya shariat se koi gunjaish nahi hai for not keeping beard?

Peel off nail polish

Q: I would just like to know if it is permissible to wear 'peel off nail polish' that you can put on after performing wudhu, and then peel off when you need to make your next wudhu, it peels off easily, also comes off in water. So would it be permissible to use and can you pray salaah with it?

Marrying a Shia

Q: I am a 28 year old female and I  feel I am ready to complete half of my imaan. I recently received a proposal from a compatible partner whom I am inclined to and vice versa. he has also met with my parents and forwarded his proposal but when my dad learnt that  he is a shia (imami) muslim my dad has silently rejected the proposal. My dad promised that  he would get back to him with his answer but it's been almost a month now and  when I approached my dad wanting to know what he has decided and as to whether the boys parents could meet with my parents his response was that I must not rush him and he will give me an answer when he is ready.  A similar incident happend when I was younger and my father failed to respond to my proposal. I don't think this is fair on both of us as we are ready for marriage and want to do things the correct Islaamic way. Are there any grounds on which nikkah can be delayed if two individuals are ready and do not want to fall into sin please can you provide me with advice on what can be done in a situation like this.

Profits stipulated in proportion to the investment

Q: There is an online company which invests in shares and money exchange.  They ask us to deposit some amount in their account. They will purchase shares with it and will return to us 3.4% of our amount on a daily basis for 100 days. They will not return to us our principal amount. If I deposit $10, I will be getting $0.34 per day for 100 days. Is this business halaal or not?

Troubled thoughts

Q: I have thoughts that trouble it may be because of what I said. If I make dua or say something for something bad (eg dont grant me jannah) (Allah forgive me) or something that may not be bad (eg Allah must make me worship him in hereafter)(Allah forgive me). Can I be forgiven for both situations and the stuff that I say may differ?