Hi there!
Your medical is only good for one year from the day you did them,NOT from the day immigration receives them...if they expire while you visa is in process,they will either extend them,or request you to do them again.
As far as I know,the criminality check that they do is a background check with the RCMP,but I'm not 100% on how the criminality checks work.as far as I know,you will have to get your own background checks from any countries you've lived in besides from Canada and then CIC will do their own backround check from any time you have spent in Canada with the RCMP.
To be honest I think it depends on who you talk to when you phone your MP's office.I was lucky enough to talk to a lady that was very helpful.she did tell me that normally they won't help unless you have been waiting longer than the processing time stated for your visa office on the immigration website (Ottawa is 15 months).
Although my MP's office couldn't do anything to speed up the process,it was a great boost in confidence to hear that she accually spoke to someone who reassured her that they are working on my application and it didn't get lost down the back of a filling cabinet somewhere!
I would say it's worth a shot and can't do any harm to call your MP.the worst they can do is tell you they can't help or not phone you back etc. And who knows,if a lot of us had our MP's contacting CIC,it might give them a push to start working on our applications instead of whatever other Visas are keeping them busy ;D
As for calling either constituency office or office in Ottawa...I'm sorry I don't know what the difference is!
I just phoned my local MP,there was two different numbers,I just phoned both till I got an awnser
Best of luck!let us know if you decide to try phone your MP and if you get any info!
-Karl