I am no instructor, so keep that in mind :lol: Per downward facing dog, your wrist should somehow “float” above the mats, with weight toward your finger tips, which presses into the mat. The wrists are not meant for weight bearing, though yes, there will be some pressure there: it acts as a conduit to transfer your weight forward toward your finger tips. This is accomplished by forming a straight line between your hip, waist, shoulders, head, arms, down to your finger tips.
My guess is that you don’t have a straight line and your wrists are more or less under your shoulders, putting undue stress onto them. Look at the photos on google - there is a reason they all have straight line, and it is not because it looks good:cool:. One simple gauge to help me ensure I have a straight line is, my arms should pass directly next to my ears (my guess is that your arms fall below your ears), with finger tips pressing into the mats, hips up, and your toes, also pressing into the mats to form an equilibrium. That way, your whole body works together, not over stressing any single joint.
Now this is NOT an easy posture, especially for people who aren’t accustomed to it. Whoever say Yoga is all relaxation - they have not done Yoga lol. You will get tired and sore in short order, until your body gets stronger. You should probably switch to happy baby often first.
Downward facing dog is a resting pose, but not relaxation pose - your body continues to work, strengthen, while stretch. Happy baby is a a relaxation pose, while you allow your body to relax and stretch. They don’t achieve the same goal, but for people having trouble with downward facing dog, it is a good pose to go to.
As to your knees, again, my guess is that you rest your knees directly on your knee cap, thus putting undue pressing onto it. Your weight should be in front of your knee cap, not directly on it, and that generally means to move your knees backward a little bit till your weight is on the bone above knee cap, not on knee cap itself. - and while you do that, you will then need to make sure to engage your core to tuck your butt under so you are not hollowing your back. Again, who say Yoga is easy:lol:?
If you still have issues - I’m not familiar with your medical history - there are many many Yoga poses you can use to open your hips: various forms of Pigeon come to mind that will target this area. Some will not put any stress on your knees. Again, you should talk to your instructor to give you alternative exercise. Not everybody can do every Yoga poses (conformation/age/injuries/etc), and there are always alternatives you can choose from.