If cutting beams with a cutting torch, guaranteed it will be warped and wowed (warped= bent in a circular fashion, wowed= bent side to side) when finished. You will have the same forces working when you attempt to weld them all together so the joint is not going to be very straight even with a knowledgeable steel fabricator and will have to be hot worked to draw it back in a straight line. Assuming that you are a highly competent welder, it could be done, but cost wise I think you are going to find it untenable to do what you are planning. Cutting 1/4" steel with a zipwheel(1/16" thick grinder disc) will take a lot of wheels at $2 each for Dewalt. Harbor freight are about half that, but last about half as long so you are going to have lot invested in just abrasive wheels.
My advice is like most everyone elses here, get a single beam the length and weight that you need for your span and avoid the cost of grinding, welding and heat straightening the drop pieces which will likely cost you more than buying a new beam.
If you intend to go ahead with welding them together, I wouldnt split them to make tees due to the warping factor, weld them together and then buy one more beam to splice in to make your length and make sure you get a good 100% penetration weld at the joints by bevelling the edges. Double V bevel the web so you can weld from both sides and single V bevel the top and bottom flange of the beam so you can get full penetration welds and weld it all from the top of the flange (flip it to weld the bottom) You would need to keep all welds equal during the welding so you will be doing a lot of flipping in order to weld everything in flat position.