I'm going to have to respectfully disagree with you here Andre. Those are HHS or maybe even High Carbon tools.
I agree with Jim - those look like cheap Chinese shanks that used to have brazed carbide bits soldered onto them and have been ground on a bench grinder. They are marred by the set screws of a tool holder and are also bent so they're soft steel.
The top one looks like a round nose tool for between shoulders work but this one has positive side rake and no back rake. Typically, round nose tools have zero rake tops so this one, if ground this way on purpose, would be used as a RH tool and will cut towards the chuck.
The second one looks like it was ground as a facing tool or knife tool. This one also has positive side and back rake and is meant to be a RH tool. It has no significant nose radius so I suspect it is used for facing. Curved shanks typically are used for clearance close to the chuck.
Both are well worn and you should take a sharpening stone and hone them before use.
Even better, buy the tools you linked in your original post and use them. While I agree grinding your own tools is a good idea, especially for a small lathe, that takes time to learn and who wants to wait for that when you have a brand new lathe asking to be turned on? Buy those new tools and learn to use them. If you hone them after each session they will last you a very, very long time. You can later buy some mild steel key stock to learn how to grind bits before graduating to HSS.
Oh, by the way, knife tools are actually meant for facing but many use them as general purpose turning tools so the first two tools in your list will face well. They have a machine-ground chipbreaker so they'll work fine but may be a bit harder to sharpen; you will need a very thin stone or a credit card sized diamond stone to do it.