What is said above is correct (both my sons just completed it with BPP in London and I am a lawyer). It was quite complicated last September to work out what was allowed as we were emerging from special covid times, but BPP also obtained permission for a second year (and going forwards for your year as far as I know) from the SRA to keep the LPC exams (if students choose) online and very early on they clarified that you are allowed to write on your BPP and other notes and then take all that into the exam. I think it will be easier this academic year as the rules are now clearly decided.
Some students choose to sit the exams in the exam hall with BPP. In both cases you can take any physical materials you like into the exam, hand written, folders, law books, BPP materials, anything at all. However you cannot take anything electronic in and you cannot print anything in the exam (not even for those sitting it remotely the exam paper and any accompanying pdf provided in the exam although BPP have also made that fairer as scrolling within a big pdf was harder on remote sitters than in person sitters with a physical pdf so they use a shorter one now).
There will be a point when you have to decide if you want to sit your exams in the exam hall or remotely (if it is the same as this academic year) , well in advance so it is worth mulling over the pros and cons for you in your own situation. It does not affect materials taken into the exam, however, other than if you have a big table at home you might have more space to spread out lots of files and would be on a smaller desk in an exam hall so able to use fewer documents. However having lots of things to open can just lose you time so it is not as simple as having vast numbers of materials means you do better.
For my sons being able to type the exam when sitting it remotely was the key issue in deciding to take the exams online (and then no issues over train strikes and covid - we are about an hour away on the tube etc to get to BPP and exams in London). However issues such as do you have a quiet place in which to take an exam at home, is the wifi good (ours at that stage was cutting out briefly once a day but thankfully it did not in the exam) and also do you do better in exams in an exam hall writing it v. observed via webcam (the main LPC exams are proctored/observed if you do them remotely and you scan the room with your webcam and show your student card and then may not leave the desk until the exam is over which is why the exams are now largely divided into two - morning and afternoon so people have the chance of a break rather than the 3 hour exams I did back in my day).
You can certainly print your own notes and put them in a binder. You can buy text books, BPP course notes you buy from anyone. you can have print outs of BPP materials in folders or stapled of each part of that module. You can have hand written notes, stickers you wrote on. You can have model answers.
(I looked up my Finals Exams out of curiosity in my diary from 1982 when my sons were doing their exams. My exams back in the old days were under the 1979 solicitor rules when we had just moved to an almost all graduate legal profession for solicitors. For that course (the one done before the LPC started) I had all my exams between 20 July and 27 July on all topics of that year's course, in an exam hall for 3 or 4 hours a day with no notes of any kind at all. We were examined on everything including what we learned on the course right back to early September of the year before. However the topics covered were very similar to those today, but without the "skills" testing. The online exams of 2022 do in the LPC reflect real life and practice where solicitors do look things up all day long but need in practice (and in the online exams) to know the law so you know where to look. So I do not have a probllem with the current system (although I am reserving judgment on SQE which seems to be a whole new ball game). )