I finished studying with the OU recently and studied with them for years. I used to have severe anxiety, I have moderate anxiety now.
Telephones, I've had many, many, many, many, many tutors and I've only ever had a telephone call with two of them, one who rang me as he was concerned (was anxiety related and how was I getting on), the other when something went wrong. Both a single time. Ever. So don't worry about telephones.
Face to face tutorials - barely exist any more, although this varies widely by subject. In 2018 there isn't very much in the way of face to face contact any more. In the past each 30 credit module used to have around 4-5 face to face tutorials in a city maybe 30 miles away. These were optional.
Online tutorials. Now it's all virtual, the latest version of online tutorials the OU uses uses something called adobe connect. Basically you sit in an online chat room, you can sit there silent and type responses in the chat box if you want. Sometimes there are as few as 2-3 other people, sometimes in large modules in module wide tutorials there can be 30-40 people. These are generally recorded, so you can watch them later. I always found it better to go to online tutorials as it forced you to watch them and was more motivating watching live than a recording later (which you felt guilty about).
Emails. Get emails at the start of the module then if you don't converse with tutors about TMA (tutor marked assignments) feedback you may only hear from a tutor by email 2-4 times in a 9 month course. I'm going to shock a lot I rarely bothered reading TMA feedback and so virtually never emailed my tutors. Other people seemed to have a very close relationship with their tutors. Many courses have 4 TMAs per module per 30 credits. Not all.
Tutors. Brilliant. I've studied at other institutions and I only ever met two 'bad' OU tutors. Often holding down multiple academic jobs, great teachers and human beings. The only downside was many were very optimistic people.
In recent years on parts of the course that require group activities, the OU's become obsessed with forums. However many people don't participate.
In terms of joining in with other students I don't have any friends I made at the OU. I have an acquaintance who wished me luck after I finished and another tutor and that was it. I never worked out how to get an open university email address which meant I couldn't join the OU facebook stuff.
In terms of anxiety I found the OU to be quite stressful as I found it very bureaucratic. I hate coursework and the OU is obsessed about it (although they have relaxed regulations the last 2-3 years). Every single module these days now has different rules on thresholds so for example to be entered on the exam one module had rules of score 30% or more in 7/10 TMAs or iCMAs. Others 40%. Others weird random rules they thought up. I did tend to do more modules simultaneously than other students, which might explain also the higher stress levels. One of the things I noticed the last two-three years is as the OU's had cuts and been changing, the formats of module websites seems to change for every module and is at time just a random splurge of noise. I noticed on my last few OU modules it wasn't just me that thought this and there seemed to be a lot of stress/questions by the sharper students about where is so and so on the website.
Exams, most non-level 1 modules have exams. If you're lucky and live in a big city it might be 3-4 miles away in the centre or at a venue or a football ground. You won't have these straight away and will be able to settle in.
What I would say is there are a lot of 'lurker' OU students that don't really have much to do with anyone else (this was a point made to me also at a consultation meeting I attended). The side the public see are the students who gush on about the OU like a religion and have supportive employers encouraging them on the course and it 'changed their life'. Nice people and I've met my fair share. For me the OU was a very lonely and bureaucratic experience and if I had the time I wouldn't do it again.