Regarding online bank statements, these are perfectly acceptable if each page is stamped by the issuing bank or building society - see IDI Appendix FM-SE (Specified Evidence) here which is referred to in IDI Appendix FM1.7:
"1. In relation to evidencing the financial requirements in Appendix FM the following general provisions shall apply:
- (a) Bank statements must:
- (i) be from a financial institution regulated by the appropriate regulatory body for the country in which that institution is operating.
- (ii) not be from a financial institution on the list of excluded institutions in Appendix P of these rules.
- (iii) in relation to personal bank statements be only in the name of:
- (1) the applicant’s partner, the applicant or both as appropriate; or
- (2) if the applicant is a child the applicant parent’s partner, the applicant’s parent or both as appropriate; or
- (3) if the applicant is an adult dependent relative, the applicant’s sponsor or the applicant, unless otherwise stated.
- (iv) cover the period(s) specified.
- (v) be:
- (1) on official bank stationery; or
- (2) electronic bank statements which are either accompanied by a letter from the bank on its headed stationery confirming that the documents are authentic or which bear the official stamp of the issuing bank on every page. " [my emphasis]
It's worthwhile for your wife to apply for a national insurance number from the Department for Work & Pensions (DWP) - this is very straightforward and the official letter with her NI number will be another useful piece of correspondence evidence.
I'm surprised about the difficulties opening a bank account for your wife. Maybe we struck lucky last May but my Nationwide branch in north London opened a full FlexAccount current account for Nok with a Visa debit/ATM card on the spot with no problems - we used our council tax bill in joint names and her Thai passport. The Nationwide staff member who handled this was very friendly and very helpful.
The time frame referred to in the FLR(M) application form (see pages 63 and 64) is up to a maximum of two years:
"Six items of correspondence addressed to you and your partner at the same address as evidence that you have been living together since your last grant of leave in this category, or from the date you first started living together up to a maximum of two years".
Your now wife came to join you in the UK on a fiancee visa for the purpose of marrying you and so it is quite acceptable that the evidence of your cohabitation is limited to the five months that you've been together in the UK. Just provide an explanation as indicated in Note 11 on page 64.
Hope this helps.