Yes, but consider whether an A-class fare (discounted first) might be cheaper, particularly on LHR-IAH, which is a corporate heavy route with a lot of policies that allow flexible business fares (which are expensive, at least publicly - but most business travellers will be on corporate rates), but which prohibit First. Shortly before travel, it's quite common for First to cost less - it has a cancellation fee and a change fee.

It depends on the exact, full fare code, but R, D, and C all offer some flexibility. I haven't seen any I-class fares with no changes permitted whatsoever for a while, but they could exist, particularly in a sale.

If all else fails, go completely flexible and start in Prague - with a stopover if necessary. What are your planned dates?