Anything involving the lifting of pavers needs to be done properly if you want it to look original when it's put back.
1. Always number the pavers when they are lifted. They fade / wear over time and if not put back in
exactly the right order it won't look right when viewed from a distance.
I've seen plenty of situations around the CBD where this wasn't done by contractors installing cables etc and it's a real nightmare even for the experienced pavers to work it out from scratch. It comes down to moving them aound like doing a jigsaw then standing back and taking a look. Takes forever so always number them.
2. Unless they are small or not too old, you need to get them the right way around too. The side that faced north needs to still be facing north. It won't look 100% perfect due to uneven wear if you don't put them back the same way.
3. If you turn one over and put what was the bottom facing up then you'll need to do the whole lot at least as far as the next path, driveway or whatever else interrupts the paving. At home that would most likely mean doing the whole lot.
4. All that said, it's quite possible to make new "old" pavers that blend in with the originals. Don't be surprised to find that one paver costs the price of a new car though by the time a sample has been analysed and the factory does a special production run just for you and then spends a lot of time wearing them out so they look right. It can be done but serious $ - a lot cheaper to not smash them in the first place.
5. Hydrochloric acid is the go if you want to remove cement. But if that's not working then I'd try a pressure washer - you'd be amazed what they will get off if you keep going long enough. Normally use cold water and no detergent but for oil spills etc hot water with detergent can be useful. Be warned though - the cleaned area will look better than the non-cleaned areas so you'll have to do the whole backyard, city block or whatever.
Note about hot water. The domestic units normally aren't suitable for use with hot water - don't do it unless absolutely sure or you'll wreck the machine. It's really only useful for industrial situations anyway unless you've managed to end up with an oil spill etc at home.
6. If the pavers sink, there's a problem. Usually it's due to inadequate compaction of the ground before the pavers were laid. If vehicles are going to drive over it then either do a proper compaction test and get a reading of at least 98 or compact, compact and compact some more. Don't forget that FCR etc needs to be wet when compacted. Rheofill (flowable fill) solves compaction issues but it's not common for domestic use.
7. If water seeps from the pavers then be sure you find the cause without delay. Apart from issues with washing out the sand etc, it may be a warning that a pipe is about to burst. I've seen a city block flooded this way and pavers go flying everywhere when the pipe finally blows (nobody hurt thankfully). Be on the lookout especially if you have any council water pipe easements running through your property.