Putting information on the noticeboard about redundancy doesn't make it 'unfair', as in 'unfair dismissal', necessarily, no.
Was there any information put on the noticeboard before you had your letter that you didn't already know? If it was just saying that you have been made redundant, which you already knew, I can't see any problem with that really. Not my preferred method of communication with team members, but it's not unfair.
And it certainly wouldn't be reasonable to expect them not to mention the situation to people pending a possible appeal, that just wouldn't be practical.
Often redundancies are on a tight timescale, and if there are other people potentially affected, they need to be told that they are safe, for example. Similarly, if people have been made redundant, how else are the employer supposed to explain their sudden absence from work? Best practice during a redundancy situation is to keep everyone as informed as possible. Rumours only start anyway and that's never good.
So no, they don't need to wait until you have submitted your appeal and had it heard before telling people, and no, unless they were telling people via the noticeboard things that you didn't know already, there's not a problem with that either.
Do you realise that you need to go through the appeal process before submitting a tribunal claim for unfair dismissal? You mention having filed the claim already, even though you were only dismissed on Thursday, is that right? The tribunal are likely to send it straight back and tell you to appeal the decision first I expect.
Focus your appeal on things that were unfair about the procedure, particularly in terms of selection. Don't muddy the waters by complaining about not receiving written confirmation until two days later, or information being posted on the noticeboard. If the decision was unfair, focus on that.