Maintaining family ties with people who don't follow a mazhab

Q: I have a few relatives. They are born and brought up in a Muslim family like us. However at present, they have converted into La Madhabi theology like Dr. Zakir Naik, Ahmad Deedat, etc. by refusing madhab theory.

My question is how do I maintain my relationship with them? Are we allowed/permitted to share non-veg food with them? Can we consume chicken or other non-veg whenever they invite us over for a meal? Are we allowed to perform Salat and Janaza together with them? While reading Namaz under our Imaam they pronounce aameen loudly after the Alhamdu....? Will it affect our namaz in anyway?

Muslims cycling

Q: It is this time of the year when a few bicycle races take place. E.g. Argus, Tour Durban, etc. Many Muslim people with big beards etc. take part in these. It is done with thousands of people all scantily dressed. Some so called pious Muslims claim it is exercise and that they lower their gaze. Allah Ta’ala knows best how they avoid accidents like that.

1. Is it permissible to take part in a cycle race?

2. On a weekly basis to cycle as a group, early in the morning, along a similar route, would that be permissible?

Consulting one's family regarding a proposal

Q: My family had got a proposal for me and I was interested but with no solid reason my father refused. He said things like, the boy's family were living far away, and also he is 10 years older then me. I did istikhara many times and I got no negative signs. I do pray daily to turn my heart away from this but it is uncontrollable now. I want advice whether I should ask my family to consider it. I'm afraid that once it mustn't get refused for a reason that is not valid.