Can a single player build a clan dojo?

Yes it is definitely possible to do a fully functional and practical Dojo by yourself. The resources can be gathered quite "quickly", quickly in quotes, because research costs 3 days to do so you have three days to smartly farm for the next thing to buy.

For a fully functional, Research-aimed Dojo you need 15 Formae, you don't need to get them straight away, mind you, and I'm sure if you don't want to research specific stuff or want it to be not as pretty as to work as a real home for your future clan you can get less Formae and start away, I'd personally start the build at 2 Formae.

Here is how my Clan looks like, built by one person, farmed by one person and started around 75% of the research also by one person:

You start with a clan hall, with 2 doors, this hall is free and requires no forma. The first hallway I start with a Reactor, then I started building all the impractical stuff you don't need to visit or even see to have a functioning Dojo, my goal was the Grandest Clan Hall which gives you 6 free doors and AMPLE space for Trading posts and the 4 useful research centers.

Reactor -- Clan Hall -- Great Clan Hall -- Greater Clan Hall -- (T-Connector leading to an Oracle) -- Grand --(Cross Connector with two reactors) -- Elevator

So basically one long corridor with all the energy needs you have and the Oracle, a thoroughly useless room you need for research. Up until now you have used 10 Formae. The elevator is the starting point for the next bit

Elevator -- Grandest Clan Hall

Now you have 6 free doors, I put all 4 research centers, Tenno Lab, Energy Lab, Bio Lab and Chem Lab on the sides of the Grandest Hall, the front door leads to the elevator and the back door leads to a cross connector, and then an obstacle course and two free nodes. Everything behind the back door is up to you entirely.

Now make Grandest Clan Hall your home and you basically have a massive room with ALL research avaible :D

Very possible. I've built 65 rooms by myself. If you enjoy playing the game and, as mentioned above, use your time wisely between builds it isn't that difficult. Forma will become your biggest nightmare though. Each room requires 1 and it takes ~ 20 minutes for even a chance of getting the blueprint for one. This was basically a majority of my time on warframe, farming forma after forma on void runs.

Yes you can. I did. I built a full 100 room clan unlike any clan I`ve see in the whole game. Also decorated them to full capacity. Decoration was done by members but rooms were entirely done by me.

100% can be done, we did it to get away from being constantly asked to play in the rails everyday. So just 4 of us and alot of mat's and forma, you will need a forma for every room. And we rushed rooms with plat also. We built one of the biggest dojo's I have seen for in that time. Put elevator going up to put your reactors in so everything you need is on the same level and have the grandest hall your main. Like all your research labs and trade and where to spawn etc. Just makes everything way more easy. Hope you's get it done.

I would say it is but def easier with more people. I'm doing this myself right now and as a fairly new player I've found all resources, no matter how rare, pretty easy to come by. The only exception to this (and the major roadblock you will encounter) is acquiring formas. These can be found in the Void, through alert missions or purchased for 20p. Asssuming you want to do this as cheaply as possible, I recommend finding a warframe that's good for solo play. Rhino and Loki come readily to mind. With a good solo warframe you'll be able to solo some of the void missions and with luck collect a few formas. Hope that helps.

I made my clan by myself before I invited members so yes it's possible. But it cost a hell of resources, expansively Formas

As leader of a Clan that was mostly made by me, I have to say it is possible, but everytime I work for my Clan Dojo I end up getting a lack of very common resources and credits, so it is possible, but not recommended.