You are aware, I hope, that you don't have to apply via the inland process - even though you are in Canada during processing. Your ability to remain in Canada is dependent on your keeping your temporary status valid - that is separate from your application for permanent residence. You can apply outland - which is faster and preserves your right to appeal a refusal - even while staying in Canada. The only drawback would be if an interview was required - you'd have to go to the overseas embassy to attend. But if you provide sufficient evidence of your "genuine relationship", you can normally avoid the need for an interview to verify that you are not just in the relationship in order to get into Canada.
As far as the police checks - you are required to submit, with your application, certification that you have no criminal offences in any country in which you've resided (except Canada) for more than 6 months since turning 18 years of age. This is a requirement whether you submit an inland or outland application - and not submitting the clearance(s) with the application will delay processing. As far as Canada and the RCMP check - CIC will do a "name check" on all applicants residing in Canada and will only require a fingerprint clearance if the name check produces a "hit". So you're not required to submit an RCMP clearance with your application, even if you have been in Canada for more than 6 months.