Important ~Bolivia Question

1) Lots of different bus companies. This is Bolivia, so none of them particularly reliable. If your planning is really critical (i.e. you will miss a flight or similar if the bus is an hour or 2 late), forget about Bolivia altogether. Anything can (and often does) happen in that country, one reason why I love it.
3) I don't know Uno, but I don't think it is on the Bolivian side. Only Isla del Sol and Isla de la Luna there, as far as I know.
4) see question 1
5) I think the airlines are the major problem with the "flight ticket required" hassle. I have never (not once) been asked for an onward ticket at any border (whether arriving by land or by air) in all of South America.

1. There are local public buses that go from Copacabana to La Paz regularly and then there are tourist type buses which are more comfortable, quicker and a bit more expensive about US$6 and takes about 3 1/2 hours. Plenty of tour agents in main street to make same day booking.
   2. Moon Valley is located about 10 Km from the city centre, its an amazing eroded hillside maze of canyons. Unless its part of a day tour, catch a taxi.
   3.The Uros tribe and their floating reed islands are only accessible from the Peru side from Puno. Isla Del Sol is only accessible from Copacabana on the Bolivian side. You can only cross the border via road.
   4. Tour Bus from Puno to Cusco takes about 8 hours. Stops at sites/sights along the way as well as a stop for lunch.
   5. No problem with border crossing
   

(2) Valle de la Luna from La Paz. You can take the tourist bus which cost USD6 to get to Valle de la Luna along with other sites of the city, the tour runs for a whole day, one to Zona Sur (Valle de la Luna) and one goes around the city. The commentary is quite interesting and it is a red double decker that departs on schedule from Plaza Isabella Catalica.

If you have the time the Valle de las Ánimas is much better than Valle de la Luna, but will require better part of a day to see.

Yep. The Valle de las Animas is better than Valle de la Luna,
To get to Valle de las Animas, take bus 42 or another one marked 'Ovejuyo' from the Plaza de San Fransisco, downtown La Paz and get off when the bus crosses the Quebrada Negra ravine at the upper end of Ovejuyo village. From here just follow the ravine going up. The Bolivian Lonely Planet has a more detailed description of the route. To get back, simply flag down one of the busses heading to La Paz.

This is a beautiful place with very strange rock-formations and spectacular views from La Paz and surrounding mountains

to get to Valle de la Luna with public transport you can take any bus from Prado going South marked Mallasa and/or Zoologico. If a smaller mini bus it costs 2.30 B if a larger old school style bus it costs 2 B. The jounrey take from 30 mins to an hour depending on teh bus type you take and the time of day.
Other options for getting there include taking anything going to Calle 8 in Calacotothen changing and taking a Mallasa bus (more frequent from here) or going to Plaza Belzu (about 3 blocks from prado but not so easy to find) and taking a bus a heading to mecapaca/jupina which passes through mallasa and by teh Valle of teh moon.
A taxi from the center should cost you 25 bols for a radio taxi , 20 for non radio taxi.

the floating islands are Los Uros, on the Peruvian side of the lake. Access from Puno. Worth a visit. Trip I did also visited funerary towers at Silustani which are interesting.

To get to Cuzco you can bus from Copacabana to Puno, then change buses from Puno to Cuzco. Or take the train- it's a stunning journey, more impressive than bus, though it takes a bit longer.
$15 US one way. About 10 hours puno-cuzco train

Yes you can by pubic transportation. Make sure you wear a condom!