1) Should I use a broker?
Depending on your LTV a broker may be able to give you more options. Its no harm to visit one and see what they can offer. You should also visit your own bank, as you are an existing customer.
2) Should I just try and make appointments to meet directly with as many banks/providers as possible?
Best advice would be Yes, but you can search online for what rates each bank offers. This is slightly harder now, as the ecb is dropping by the month and rates are changing quicker than some websites can keep up.
You can ask a broker which banks do they get quotes from, if you realise they dont quote from X bank, visit that bank, just to cover yourself.
3) How can I narrow down my search to those who are most competitive today?
Broker and Online,
www.mortgages.ie. But visiting the bank itself will give you what todays rate is.
4) What are the fundamental criteria I should use to evaluate the offers from the financial organisations?
Go with whats lowest (cheapest) dont feel like you should go with X bank as you think they are a "better bank" but they are dearer.
5) How much room is there to negotiate with banks on the assumption they favour a 'strong' client?
LTV is really the only factor these days. Your own bank may do a better Fixed rate seen your a established customer, but in the current market, Standard Variable is best.
With trackers gone, i dont think any bank will negotiate on standard variable.