Sorry for dealay - I was editing when I had a
on keyboard moment! Fortunately I had a spare.
There was also another keyboard!
Sounds fine. Your time in Kaz and Mongolia will count as days out of RUS, and be added to the days from Visa Validity date to Entry to Rus.
An invitation takes a week or so to be issued in Russia. It is possible to then get the Invitation sent to the Embassy by telex at a similar cost to DHL - £35ish. It is then possible to get a completed and accepted visa application processed 'next day' for even more!
You will need an Agency to get the Invitation. The going rate for the inviting company is currently about Euro50-60. Your agency will want their fee.
After that you can do it yourself or continue using the Agency.
You need a UK Employers letter confirming you are going on their business and they will cover any costs you do not meet. (Get a friend with some letterhead to do it - they never check). Alternatively you can be self employed and produce an original, current, bank statement showing a balance at least equal to £100 per day of the visa validity period.
Being a UK citizen you don't need medical insurance, so answer 'no' to that.
Whether you do it or your own agency does, the application must be made through the Russian Embassy's own Handling Centre (that you pay even more money to). Full details here Russia Visa Information - UK - Home Page