I would like to glue it to the tile that is already there, except remove a few that are coming loose.
yes,but----------------don't you hate that line? the linoleum will only be as solid as the tiles under it. as they come loose in the future your linoleum will end up with loose spots that can bubble up, catch and tear if you slide things across
yes, but, if theres already some of the old tile coming up, may be a goo idea to take all of it up. if it is only a couple of pieces just pull them and fill in with leveling compound
Bill's answer is correct and in addition to it I will add that depending on where you live it could be against the law to remove it due to the asbestos. It's possible that the law requires you to have a company that's certified with asbestos removal come and remove it. However is anyone going to question you if you DIY? If so there could be some stiff penalties involved. If not than the other thing to consider would be to use a quality dust mask because you don't want to breath that stuff in at all..... We covered our floor insted of ripping it up.
Sure you can lay linoleum over the tile, but instead of removing the loose tile I suggest you glue them back. Liquid Nails will do the job. By all means ware a mask while working with the asbestos tile. Be careful about what type linoleum you buy because it can have some asbestos in it, but not at a hazardous amount. Go to the web page below its very informative. Ever who you get the linoleum from make sure you tell them what you are applying it to. Be sure to ask about what type of notched trowel to use and the mystic. If there are large seams between the tile make sure you get enough mystic down into them so you want see their indention's when the mystic drys and shrinks. To really be safe cover over the tile with 1/4 or 3/8 inch ply then put your linoleum down.