This all sounds an horrendous faff.
Perhaps next time consider buying cast aluminium furniture. We have now had 2 sets for more than 10 years and they still look like new.
Tricky to get good versions without the massive cost in France, but in UK these guys are excellent:
https://www.gardenfurnitureworld.co.uk/gardenfurnitureworld/hartman-cast-aluminium-furniture.asp
The turps is there to help the oil sink into the wood - it will stay absorbed in the wood and protect it. You add a bit more turps in the first coat, then less turps in the second coat.
I use oil a lot. It does make most wood look good, and it’s easy to use, easy to revive, and good protection. However, that furniture looks a bit grey - you could either use a stain first, or go for paint.
In my experience of marine teak varnishing it is the last thing you want to do. It looks beautiful to start with but because of the nature of the wood it never bonds properly and will soon start to flake and look awful. The great advantage of teak and other exotic hardwoods is that they do not need a protective coat, the oil is cosmetic.
Time will tell, David, but this is a sealant rather than a varnish and does appear to be different according to reviews and the reccomendation of teak furniture suppliers. You are right, of course, the natural oils in the teak itself will protect the structure of the wood and it is actually for that reason that oiling it is not recommended as I understand that it will result in a deterioration in the naturally occurring oil. Both approaches are purely cosmetic at the end of the day and what I am aiming for is something that does not discolour, which discourages or prevents algal growth and ideally sheds water so that the furniture can be used shortly after it has rained.
It sounds as though you’ve found a good product. The worst that will happen is that it might need redoing in a few years. 
You really should thin the linseed oil with turpentine. If you don’t, it takes an age to dry properly and can stay sticky for several days. The turps helps the oil soak into the wood. I did my decking with a 60/40 mix of oil/turps and it was dry in 24 hours. Also our many ants didn’t go near it.
Now I’ve read the rest of the thread, I see someone mentioned Siccatif, which I also used. I was advised not to use white spirit instead of turps and took the advice, even though white spirit is MUCH cheaper.
Not only mentioned by posted a picture.
Hello Graham,
In your opinion, could one use the clear Sikkens on an oak front door. Or would that boat clear vanish/ paint be better?
Thank you, Fiona
I thought that marine varnish would be great for both my oak front door and my hardwood shutters. It was not. My house has all its windows and shutters on south facing walls and I underestimated the effect of exposure to the summer sun. One pair of shutters spends part of the day in the shadow of a barn and those shutters have lasted for years without attention. I removed the varnish from one door and repainted it with Tollens white paint. It was not cheap but it does seem to be up to the job.
Don’t see why not tbh. Is it a solid oak door?
You could ask here
Just to add, Vanessa’s parents used boat varnish on their wooden front door (being boat enthusiasts in sarfend) but he had to redo it frequently (she recalls) as was the case with their sailing dinghy. Vernis here tends to blister quite easily with the heat of the sun whereas the sikkens has shown no signs of that whatsoever.
My Dad used Spinnaker Yacht varnish on his boat.