Well, I'm secondary so you'll have to take what makes sense for you. Most children already have an EHCP in place when they get to us and it's unusual for us to start from scratch. Happens occasionally though.
Progress - we base our Y7 support on previous primary support or Ed. Psyche. recommendations. For most children with some tweaking/experimenting this means progress continues at an appropriate rate. However, if this doesn't work for the child, or us, and they need more we can, and do, use progress (or lack of progress) as evidence for requesting more money to offer additional support. Also, sometimes at secondary progress is harder to map accross different subjects with different teachers. So, for example a student might make huge progress in History but very little in English. It can be difficult in cases like that to explain how this can happen - it can also be difficult to justify to the LA why that child should be entitled to support in both lessons still.
Each child on our LS register has an electronic file where we store every single piece of information about interventions we do, including pupil feedback afterwards. So we file what for, what done, who with, problems arising or progress achieved, report from adult who ran intervention and their suggestions for next steps. We also track their reading, spelling and comprehension ages at least termly. If they have numeracy/communication/language/speech issues etc. We file the appropriate test results for that too. We file reports from specialists, emails from home (most parents email rather than call) but we also log phone calls including what was discussed and why. The more evidence you have, from the more people you can, the stronger your case will be.
As for time scale, I think different LAs have different criteria. Our's (I believe!) has a notional two term expectation before they will consider an EP visit etc. for new students (Y7 or otherwise) but they have come before then in emergencies (tend to be out of school but real life/death or criminal behaviour worries). In our LA EPs advise whether they feel an EHCP assessment is appropriate - and I (or the pastoral lead) would start an early help form from that. I've never had an EP disagree with me that an EHCP is required. So, we think our system must be working. I can also ask for an EP to visit but make it clear that it's for advice without starting the EHCP process. They will come - but I have to wait longer.
I hope something there is helpful - if nothing else remember to record everything and file it really well!