As I live in Scotland, my events will be restricted. I am too late for Manchester, I am assuming so am entering Robots Live Grantham and Stevenage, also a Featherweight I have a concept and design for called Alligrator.
Applications stay open as I understand it rather than a defined cutoff period before the event (though for safety's sake, I'd recommend signing up at a minimum of 3 weeks before the event). I was able to signup for EXR Glocuester 2017 at about that time and still received the EO e-mail about it so I wouldn't say that you were too late for RL Grantham or Stevenage.

Not yet applied for [...] Kinematics Marlow if it is the EU event. Most events are Featherweight and the Beetle is a side event I assume. Any other events you'd recommend?
June is when the applications open for the EU championship so I would keep an eye out for that (something I fully intend to apply for). UWE occasionally hold Beetle Brawl events so there is that as well. Beetleweight events do tend to be side events - they were at RL Grantham 2017 as I recall and RL Burgess Hill runs one as well.