First of all, all the best to your friend.
Now to your questions...
Of course it's safe and worthwhile to cycle by yourself. There are many advantages to being on your own - having the freedom to stop wherever and whenever you like is, in my opinion, the main one.
If you're travelling alone, pack a good first aid-kit and keep it handy in case you need it! (Not trying to scare you, just when travelling alone you need to be responsible for the worst case scenarios). And some snacks. There may be times where you'll want to stop for an hour or 2.
There are other cyclists all along the Camino. From my experience, most were couples or groups. Joining in is sometimes possible, but to find another rider who travels at the same pace as yourself is a bit like looking for the proverbial needle in the haystack. I wouldn't count on it, but nice if it works out.
You've had good advice about interacting with pedestrians. Perhaps not suitable language for a Camino, but I've cycled all over Europe using the motto that everybody else on the road is an idiot - It hasn't let me down yet.
Travelling on a bike has one disadvantage over walking - and that is the "social" side of the Camino. After the first day you'll have left "ÿour" group behind. So every evening you will be the "New kid in town".
As for your time frame, the 13 days is entirely doable. Your choice of route depends very much on the load you are carrying and your experience of riding your bike off-road and with a load.
If you have little experience you may want to consider staying mainly to the roads. A little bit of planning and you can check off all the places on your hit-list.
More experienced and you can seriously consider the pedestrian path on the proviso you understand that you will not be moving fast. You'll be looking to average 60+ km per day on a fairly low average speed.
Firstly, sometimes the path is right beside the road. In that case it makes sense to take the road.
If you look around you'll find blogs and Youtube videos of people who have done this and they'll offer advice on what sections to ride the road.
It also depends on your bike, it's tyres and the load you are carrying and where it is carried. And your experience. If you misjudge your skills and crash you're only hurting yourself - unless you crash into a pedestrian!
My experience is to ride what's in front of you. Pedestrian density and weather (specifically heavy rain!) can turn a perfect cycling path into a nightmare. A tough climb over rocks and little boulders can be hard work, but very rewarding when you've dragged your bike all the way up!
Whatever about ascents, I think just about everybody's advice is to take the road for the descents!
In other words, unless you need to plan to the last detail, I'd suggest that you take each day and each section as it comes. Navigation is never a problem and if you find the path too uncomfortable for whatever reason, you can always turn around and take the road.
Pedestrian traffic is heaviest in the morning when all the pilgrims are leaving all the Albergues and heading off. Depending on your morning style you may want to linger over a long breakfast and head off when the pedestrians have spread out, or take the road to get ahead of them. Hint; Read the
Brierly guide and aim for Albergues that are mid-section. A large percentage of Pilgrims take
Brierly to be the fifth Gospel and follow his sections religiously.
The last 100 km can be very busy. Perhaps not so much in September. It was so busy when I biked it that I took to taking the day off and cycling in the evenings when the path was clear. Glorious riding! September, though, the days will be shorter.
While 13 days is doable, by road or by path, I'd imagine that you could be feeling the pressure to make time, that there's a focus to get x kms under your belt before you can relax. That can easily lead to a feeling of pressure. Personally, I think that's a shame on any long-distance bike trip, especially a Camino. A big part of the Camino for me, was slow progress, frequent stops and plenty of chats along the way.
If you're in any way fit, you can make good time on the roads. Worst case scenario, most buses will take a bike in the baggage section underneath.
If time stress is a thing for you, I'd suggest you do some research on what places you specifically want to see and take detours from the road to see them. And leave a little room in your plan for when you find those unexpected places that speak to you. You'll be glad you did.
My own experience is that I did the CF in May/June 2015. I had 4 panniers and a tent (the Camino was only a part of my trip), totalling about 20-25 kg.
I used a cheapy hybrid bike with front suspension and 1,5 inch tyres. (Doing it again, I'd use larger tyres for offroad)
I followed the path most of the time (excluding descents). However, I did most of my riding when there were few pedestrians around. I covered a lot of the road as well then doubled back and followed the path. I prefer the path for atmosphere and sociability.
I took, I think, 16-17 days St. Jean to Santiago.
You're in for a great experience! Enjoy!
Buen Camino