EE offers a basic PAYG SimLINK which doesn't require a credit check. But it no longer offers 'traditional' PAYG (where a customer tops up using credit and uses that for calls, texts and data), but it does offer data packs which start from £10/month and last for 30 days with any unused data being rolled over.
The cheapest EE Sim costs £12/month and it currently offers unlimited minutes & texts and 5GB/month data over a 12-month contract. See cheap EE Sims.
Yes, you can keep your old mobile phone number. If you're moving from another network, you'll need to text 'PAC' for free to 65075 to request your PAC (porting authorisation code). You will need to provide this to EE which should move your number over within one working day.
If you are already an EE customer, you'll need to fill in a 'keep my number' form on its website.
Anyone joining EE after 7 July 2021 will pay £2/day to use their allowance within the EU. Alternatively, if you're going further afield, or plan to use your phone in the EU for more than 5 days, EE offers its Roam Abroad Pass for £10 and it lasts a month. This allows you to use your allowance in the USA, Canada, Mexico, Australia and New Zealand plus 47 EU countries. For more info, see Cheap Roaming.
Yes, EE offers 5G on all its Sims. However, be aware you'll need a 5G-compatible phone too.