Do you think depression and anxiety can be healed without medication or seeking professional help? can it be healed by sheer willpower?

It probably depends on the individual. Some people are better equipped than others to deal with depression. That's not a judgmental opinion but just a fact.

It also depends on the type of depression. Reactive depression (eg a reaction to the loss of a loved one or the break-up of a romance will lessen more-or-less rapidly) while clinical depression will almost certainly need professional help.

It may also be possible to alleviate (rather than "heal") depression by adopting a different life philosophy, perhaps based on a more spiritual outlook. But "spiritual" rather than "religious" which may simply add to the problem. Buddhism and the more spiritual aspects of Yoga might help.

Not clinical depression or anxiety. It is not a matter of choice or willpower .. It is a chemical imbalance in the brain.

It could be as plausible to "will" yourself "healed" as it would be to "will" yourself taller or to "will" your  eyes to change colour.

It depends on the cause.  Depression or anxiety caused by an event or a loss of some kind, can be recovered from with time, and usually by talking to people, such as family, friends, or a support group.

There are those that have chemical imbalances, medical issues, or have huge traumatic events that will need more help. 

Unfortunately sadly NO😔.

Doubt it i have been dealing with depression all my life in 1990i started psych meds it helps but no majic pill

Not possible.

ive been dealing with both my entire life and heres what i have learned there is defently a genetic component and your environment will make or break you if you are fortunate enough to be in a healthy and supportive environment it will make things far more easier

Here is one of the best Ted Talks regarding Depression:

She is a great comedian and communicates her points well.