If someone gets laid-off from a job and if he doesn't apply for unemployment benefits right after he is laid-off because maybe he doesn't feel like he needs the unemployment benefits since he has plenty of money saved up to last him at least 3 years without a job before he goes broke and doesn't want to go through the hassle of applying for unemployment benefits right after he gets laid-off, will the unemployment benefits still be available for him to apply for when he does need it and he is still unemployed?

yes

used it several times in my life and if they axe how much you have saved say $350

Did other people try to discourage you from applying for unemployment benefits, like maybe family members? Did you have to go to the unemployment office and wait in line to pick up your unemployment checks and were you asked how your job search is going or have a brief interview each time you went? Did the unemployment office keep tabs on you while receiving unemployment benefits, such as called you once in a while to know how your job search was going? Does receiving unemployment benefits negatively affect the applicant's chances of getting a future job?

Dude you literally pay into the system out of every single paycheck. Use your unemployment!!! THERE IS NO SHAME!! You are literally just getting back your own money which you paid into the system. If you don't apply for them you're an idiot and the government will just find another way to waste the money. Even if you don't need them, use them. That's what they're for. It's your own money!

I'm planning on moving out and buying my own house or renting an apartment in 4th quarter of this year or sometime next year. I've been thinking about this for a long time already and saved up. If I receive unemployment benefits will that hurt my chances of buying a home (getting approved for a mortgage) or renting an apartment?

Logic - it's ideally a community pool for when you're stuck between a rock and a hard place.

Most normal people are not looking to be on unemployment benefits full time anyway - so I don't see how it's 'the same' as being like somebody who's mentally ill (laziness is a mental/spiritual illness IMO) if you're KEEN to work but are having sh*t luck.

Loan: Of course it will. Why would a bank lend a large sum of money to a person without a stable job/income and long-term ability to pay back the loan?

Rent: Depends on the specific landlord.