Can you help with very dark hollows and lax skin under eyes, with hollow temples? (Photos)

At home peels like cosmelan, enlighten and aerify along with dermarolling (MTS roller with anteage MD ampules) should be started now. There are many things you can do to treat under eye hollows and dark circles. A surgical option to remove skin and/or fat will such as lower eyelid blepharoplasty with or without fat pad repositioning will be the best long term. There are many things you can do to treat under eye hollows and dark circles without surgery. Non invasive less downtime options such as fillers (Belotero, Juvederm Volbella​), lasers (Moxi/Halo/Fraxel/CO2​), Renuvion (J-Plasma), microneedling/PRP, stem cells and microneedling RF like Fractora PiXel8 or Morpheus can all help give some improvement. Accutite can often be used or stronger lasers like erbium or co2 spot treatment can tighten the skin and give very quick improvement in wrinkles and texture. A surgical option to remove skin and/or fat might be the best solution long-term. I suggest you get a formal consultation to see what is best for you and your goals. Best, Dr. Emer.

You have pointed out some questions that many others have. Do not worry, there are also many solutions to these potential problems. However, I think you should be evaluated in person by a physician or a surgeon before any definitive diagnoses / plans can be made.
Dark Circles generally are caused by discoloration due to thin skin, underlying vasculatures and inflammation. With decreased volume due to age and genetics, they become more obvious. As a start, if you can get your nasal allergy under better control, it will decrease the inflammation, which in turn reduces redness and vascular appearance around your eyes,. The discoloration and thin skin can be treated with a few different lasers / resurfacing treatments. It will additionally change the laxity and crepiness around the eye.
You have noticed a general decreased in volume of your face. This is most pronounced in your eyes (sockets) and in your temples. You can consider filling these areas using hyaluronic acid fillers. You may also benefit from biostimulatory type of dermal fillers such as PLLA (Sculptra) or PCL fillers (Ellanse; this is not available in the US but I heard it is available in Europe). It may be longer lasting and more natural for you.
Of course, if you want a more definitive treatment option, fat transfer coupled with skin resurfacing treatment can give you potentially longer lasting and natural results, where all of the areas will be filled at once with volume and rejuvenated with adipose-tissue associated grow factor/stroma. Again, adding resurfacing will address any further skin laxity and crepeness, which hopefully will give you the look you want.