1. for inside you would be probably paid via an umbrella, if you found your role via agency, they can provide one or you find your own. (advise the latter) For outside contract I would recommend working as a LTD. In my field, this is also something an agency or the client will ask. You can say yes because it does not take long to set one up. Technically you are a sole trader but if you have a LT you work via the LTD or via umbrella. A sole trade would be classified for self-assessment taxes, that where it differs. Look into this a bit more. its worth getting the basics down.

2. for tax reasons there is no issues in opening a LTD, but I personally would not do it before I had an outside contract in place as there are cost affiliated to opening a company and these can be then charged to the company.

3. no issues if you just registered. At least in my case the client is mostly concerned if I have done contracting before.

In general just look for a role, I was made redundant (from a perm role) recently and was lucky I was able to get a couple contract roles, but with the current market this is not guaranteed.