I'd recommend booking via eastcoast.co.uk (which is the franchise for the East Coast mainline -- London to Edinburgh, more or less -- but sells tickets for the whole UK rail network). For your qn. 1, their search tool has an 'avoid' option (click the 'more options' button to see it) -- though I should say that I've never used that feature, so I can't vouch for its effectiveness. For your qn. 2, their booking system has an option to add a bike reservation --- it appears on the page where you have an option to reserve a seat (again: it's a little bit hard to spot, but it is there: just above the place where they try to sell you some bus tickets...). You're told whether the bike space is available before you have to commit to buying the ticket. You'll be given a booking code, which you can then use to collect your tickets from a machine at the station when you get to the UK (you need to specify the station, but it shouldn't be a problem that Slough isn't an 'East Coast' station); you need to make sure you have the same credit card with you as you used to pay for the tickets.
One thing to be aware of is that all the train operators have slightly different rules about bike carriage, particularly when it comes to reservations (some -- e.g. Virgin -- absolutely insist on reservations; some -- e.g. Cross Country -- have a reservation system, but will let you on without a reservation if there's space; and some -- e.g. London Midland -- just operate a first-come-first-served policy, with no reservations at all). In other words: don't be alarmed if the booking doesn't have a bike space for every leg of the journey (but do double check that you have reservations for any bits where reservations are compulsory). Such are the joys of our privatised rail system!