Hey mia, welcome to VF
I would recommend consulting a registered dietitian and not someone who calls themselves a nutritionist as it is not a regulated title in most countries and most of their advice may not be evidence based.
Just going on what you have posted it seems that you are quite active and slightly underweight. This means you are probably in a negative calorie balance most days. So you need to eat more. Maybe add a shake loaded with fruit, flaxseed, soymilk and some protein powder a few hours before you train and maybe add in a bit more fat at every meal. Training wise, if you want to build some muscle you may have to cut down on the cardio a bit as that volume (3-4x a week) is usually counter-productive to muscle gains.
Hair loss can be attributed to many things, so you should probably get a blood test, but zinc, iron and vitamin c deficiency can contribute to it. And these are all easily addressed with vegan foods. Check out this
article on hair loss by, Ryan Andrews, a vegan dietitian.
"When you are born, you are set forth to die. The fact that you live or don't live between these two dates depends solely upon your own will, opportunities and desires. The weight exerciser, of course, indicates that he chooses to live." Joseph Curtis Hise