Leaking taps

I have a problem with two leaking taps one in the laundry tub and one in the kitchen sink, I attack photos of both. The problem with the kitchen sink tap which is combined hot and cold with one handle is it drips in every position. I cannot get the top off. There is a small hole just below the handle which may have once held a screw but there is no screw there now!! There does not appear to be anything in the hole. I have tried all types and sizes of screw driver but there is no result!! DO I need to get the top off or is there another way I could fix the drip. The drip is from the spout.

The problem with the laundry tap which has seperate handles is a drip from the spout even when the taps are turned off hard. Addmittedly the harder you turn off the tap (we only use the cold tap) the less the drip but it still drips. My problem is when I tried to unscrew the main body of the tap it is stuck. There does not seem to be any way to unscrew it but one which is to unscrew it from the main pipe attachment. I asume it should be unscrewed anti-clockwise but I have tried both ways to no avail. I have sprayed it with WD40 and waited and sprayed again for a few hours but no avail. My question on this tap is would it be worth waiting a lot longer for the wd40 to work or would some other approach be better. I saw a reference to PB Blaster on this forum but I have not seen it in the shops here (Brisbane, Australia).

Many thanks for taking the time to read this post and appreciate any info
Cone.

p.s. I have recently replaced a pair of taps in the bathroom hand basin. The warm water one works well but the cold water one makes a loud hissing sound when turned on and when you turn it on more it hisses more loudly. I tried knocking the stainless steel seat in as much as possible since it looked slightly uneven - this seems to have worked to a limited extent in that it does not start hissing until I turn it on further than it did before - but the hissing is still a loud problem - any suggestion much appreciated.

Finally would greatly appreciate your comments on two other issues. Firstly whenever I turn off the water supply at the mains to mend leaking taps I still find water coming up from the pipe and flooding the basin albiet it slowly. Why do you think this happens? Secondly whenever I turn on the hot tap either in the kitchen, bathrooms or laundry I can hear dripping in the roof - this stops when I turn off the hot water - what could be the reason for this?

Best Regards
Cone

Leaking Types missing photoes

Sorry I forgot to post the photos - I tried to attach them to this message but they are too large c 850kb each!! so I am trying to reduce them and will post them on as soon I am able to do it
Cone

The handle of the kitchen faucet will take an allen wrench not a screwdriver. In most cases if the faucet spout is hard to swing left and right and is crudded up, I recommend you just replace the whole faucet. It is just as easy and then you haven't spent good $$$ just to have a crudded up old faucet that doesn't drip.

You can try replacing the washers on the laundry faucets but again you would be better off just replacing them. If the connections are threaded and not soldered you can do it with a pair of channel lock pliers.

Your main shutoff valve also needs to be replaced, use a ball valve when replacing it.

Dripping in roof

It's probably not dripping, but the noise the hot water pipe makes as it expands and rubs against the house framing. Easy to fix if you can get access to the attic and follow the route the pipe takes. Or you can ignore it. If it were really water dripping, you'd probably see evidence of a leak by now.