Cross handle hansgrohe faucet I can't remove top piece

Almost certainly the hose. They leak from the bottom, cartridges drip from the top. That unit is discontinued.

https://www.manualslib.com/manual/13802/Hans-Grohe-35807801.html

https://www.google.com/search?q=Hans+Grohe+35807801+kitchen+faucet+parts

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Yes you need to replace as a complete Cartridge Repair Kit. Once they wear, you can't fiddle with them and make them better.

tighten the screw inside the head

Most Hansgrohe faucets or handles have a plug in them. This does not come apart but in most cases you simply push the plug into the handle and once you have removed the hendle you can retrieve the plug from inside the handle or on top of the faucet. If you need further help fell free to contact Hansgrohe Tech at 1-800-334-0455 press 2 for Technical.

The 14010 faucet does not have any adjustment for handle tension. It uses a cartridge to control the on/off functions. If it is hard to turn on and off it may mean the cartridge has debris in it or has worn out over time. You may need to replace the cartridge. This should be part number 92730000. List is $48 and it is available through your local dealer or online dealer. If you need further help feel free to contact Hansgrohe Tech at 1-800-334-0455.

This is most likely a cartridge that has worn out and needs to be replaced. Most of the kitchen faucets use cartridge number 92730000. This is available through your local dealer or online dealer. If you need further help feel free to contact me at Hansgrohe 1-800-334-0455. Press 2 for tech and ask for David Scarborough.

If the handle is hard to turn it is most commonly caused by water deposits in the handle or in the cartridge below. I would try removing the handle to ensure it turns freely when not installed on the faucet. If not you can clean it with CLR to remove the water deposits that are making it difficult to turn. If the handle turns freely when not installed you will need to remove the cartridge and inspect it to ensure it is not broken or damaged in any way. There could be debris in the cartrige that has either made it hard to turn or broken the ceramic disks. Our handles are easily removed by turning the bell shaped ecutcheon below the lever or cross handle. There are not set screws that hold them on. If you need further information feel free to call me at 1-800-334-0455. Press 2 for tech and ask for David Scarborough.

First you will need to tighten the set screw all the way back in. The use your 4mm hex wrench to turn the screw 4 complete turns counter clockwise. Then remove your hex wrench and the handle should come off. There will be a dome shaped cover with blue and red indicator marks. This will simply pull off the cartridge nut. It is held on by o-ring tension only. Once removed you will see the large hex head of the cartridge retainer nut. Loosen this nut and the nut and cartridge will come out of the faucet. Don't be alarmed if your new cartridge is smaller than your old one. There has been a design change in the cartridge so it will fit smaller bodied faucets but will still replace the older thicker cartidge. If you need any further information feel free to give me a call at Hansgrohe. 1-800-334-0455. Press 2 for tech and ask for David Scarborough. I'd be glad to help.

If this is a widespread faucet you will need to turn the bell shaped portion of the handle counter clockwise to remove the handle as one unit. Then you will see the hex nut of the cartridge that will unscrew counter clockwise to remove. If this is a single hole unit you will need to loosen the set screw on the handle to remove it and then remove a cover ring to access the cartridge nut. If you need any further assistance feel free to call me at Hansgrohe. 1-800-334-0455 press 2 for Tech and ask for David Scarborough. I'll be happy to help.

where are they leaking from?
if they're leaking from underneath, repace the suply lines [between the valve and faucet]. if if from the faucet itself replace your cartrage[s].