what next after trip to beach?Nope, bugfix only.
Enable the console then open it while playing by pressing SHIFT+O
That way too vague, just talk to her, do what she asks of you and then eventually you'll go on the beach trip.
Nope. Just that one BJ scene.
Practice makes perfect. You'll eventually get it, I can't imagine someone's reflexes being so shit that they'll fail that mini game. It is also definitely worth it IMO.
Your save is fucked if your relationship with mom is higher than 4/5
That bug has been corrected in v0.5c