In the "can I build a rifle" questions, the answer is "yes" with reservations.
As above, what you're actually doing is assembling a gun from parts.
The most home built guns around are the AR-15 and AK-47 series rifles.
A good many people have assembled AR-15 rifles, and the job is not all that complicated.
True, you DO need the knowledge of HOW to do it, and the tools to do it.
The AK-47 is being built from European parts kits, composed of a de-milled AK rifle.
You "build" a receiver, and assemble the parts to it, and you have a shooting rifle.
These AR and AK building projects are so popular that there are books and entire internet sites dedicated on how to do builds.
In the case of the AR-15, you buy a lower receiver from a gun dealer, since that's the part with a serial number, then you buy the upper, barrel, and other parts and basically just put them together.
Tools are not too expensive, and there's surprisingly little fitting needed "most" of the time.
The AK rifles are being built with receivers that are a flat piece of steel with the holes cut, in which case you actually use bending equipment to bend the metal and make a working receiver.
Other unfinished receivers are a piece of steel channel bent into shape, but with no holes.
By welding, riveting or screwing the receiver together and attaching parts, you can actually build a surprisingly good quality AK rifle.
The outlay for tools can be expensive depending on what you buy and how good you want, or some internet gun sites are advertising "build parties" where people get together and use each other tools to assemble rifles.
Again, this IS very possible to do and a good many people ARE doing it, and it's legal to do so, as long as you follow the rules.