Those are big items so they might make you pay taxes. Taking TV can be a hassle. I have not done it myself. If they see a bigger size TV, they might make you pay custom fee per inch which can get to thousands of rupees. Also I heard that TVs get damaged for more easily especially if you are bringing really big ones. I saw several Nepalese bring tvs (looked like 32 inch) and it looked like they were returning home from middle east. If you bring a tv from the US, the system may be different as US uses different system.

IDK about bicycle. My assumption is that you might be able to find a good bicycle, second hand, in kathmandu that tourists left after using for few days or weeks.

I took a projector with me last time since it was more convenient. If you can find a HD projector on sale. You can put a projector into your luggage or carry on. If you are really interested in getting a big screen tv then you can buy a new tv in Kathmandu. Getting a 4K tv is expensive and since the channels are not ultra high def, you are basically paying for the tv to watch occasional movies in. You can find a regular HD tv at a resonable price. I saw a 42 inch LG tv at a showroom in kathmandu around 80k rupee.