Usually bank approval for housing loan they will look into your credit score and of course your earnings.
As of now, high possibility of tad easier for loan approval due to rate cut.
And you will need to prove your stability in income with your income tax. (The approval level is different bank by bank)
I would suggest using of credit card so that they at least know you are good payer.

Are you bumi? If so, max out all those bumi fund 1st (sorry can't remember the name).

Provided EPF giving average 5.5% interest for 30 years and monthly contribution of at least 700, it is possible to reach 600k. (I'm just doing rough calculation by head, so take it with a grain of salt)

My assumption of free lancer is flexible of time. So use the time to learn more about investment or even do some business as in sorta like reselling product or part time jobs.

How long until your parents retire and how close are they clearing their loan?

Don't sweat too much about property for now. 400k house, installment around 1.9k. including all fee, total payment by your around 850k.. take your time to build your wealth and dream house. Plus high possibility your parents house will be inherited by you. Save you a huge chunk of money.

I think you are doing fine on your personal side, seems to me that your bigger problem comes from your parents. It will be difficult for you to control them since they even take personal loan..

Their house still on loan, are they not planning to pass it to you after they are gone? ( I assume you do not have other siblings)

For your action plan, that is consider good too but if you want more details then maybe can PM to talk more

hm.. i'll play the devil / bad cop here 

1. There seems to be some missing costs in your monthly expenses - eg. obvious one being rental (room or entire apartment/house)
Must be realistic to plan cash flow ahead consistently
eg. even if staying with parents please factor in IF U are by yourself - how much will it cost U?

2. When should one start thinking of buying own home?
Any time - to build-up savings, income, etc in preparation to execute
When should one buy is another question +where +how much.

3. Rule of thumb - your housing cost (mortgage+cukai taksiran+cukai tanah+maintenance+etc.) should NOT be more than 30% of your net income (active income +passive income if U choose so).
Reason - the lower the %, the less of a pain it is to own it +more flexibility in investments.
Note - a home is a cost, not an investment. Yes, it's considered an asset but an asset that sucks up cash flow unless U sell it and hope for profit. Investment properties are different animals.
4. Personal opinions on your action plan:
- Place 30k into OCBC 360 (4.1% p.a.) (emergency fund for family, need to be liquid)
Good - never touch this unless emergency.
And NO, your parents unable to pay their personal loan isnt an emergency. Personal loans and the likes are unsecured loans and choy choy if anything happens to debtors of unsecured loans, banks try to go after what's left of debtors' estate. Sorry for being obvious & fatalistic here ya

- Remaining 15k for investment (ASNB ASM1 ASM2, unit trust, ETF StashAway, Stock)
U better have some sort of equity asset sub-allocation plan & execution here.
ie. dont "all-in" into one-hand like 1 ETF or 1 Stock.

- Each month allocate 2k into investment, 1k into saving (FD/OCBC360)
increasing your emergency buffer until?
gotta re-direct the cash into investing after U reach your emergency buffer goals else U'll never win the game playing defence only. Playing good defence is good but offence is needed too to score goals and win.

- 6k-8k per year into EPF (ultimate aim is to have ~600-700k in EPF when I'm around 55 years old, by compounding I hope this is doable...)
EPF, assuming i am self-employed (freelance, no employer EPF right?), i'd treat EPF as my bonds / Fixed income portion of asset allocation & i'd also go for the max tax-relief $4K pa or more (assuming it meets my asset allocation %).
Whether or not it'll hit 600K-700k when 55, can simulate easily with a spreadsheet. Just assume 5%pa or 4%pa returns to be prudent, even though averaging about 5.5%pa

Hope the above helps in clarifying your thoughts/plans a bit without being too much of a bast*rd/hard knock 

I'd suggest not lumping up all problems and trying to solve everything in one shot/plan - ie. noticed i didnt bother stating possible solutions about your parents' home loan and stuff?
Plan A first, things that U can control / foresee enough
Then adjust Plan A for parents' stuff and see if can do Plan B - coz U can't control others +others may not want you being nosy/your help.

afaik, those asbn are damn hard to get for non so i just gave up. but you are welcome to try. its good to have
meanwhile, brush up skill/knowledge which type of investment as you mentioned initially suit your style/appetite

hmm.. some tradition handcraft product which earn them 10k a month. please do check if its due to world event or product itself causing the sales to drop.

i guess they have their own reason/pride not wanting to disclose all. i guess all you can do is save up just in case they needed your help. just make sure they are not late with the payment.

its hard to answer, everyone's view and situation is different. but i would advice never go way over your head.
you need to have buffer if you ever consider buying a house. when market is good, earning 10k, market down, earning 2k.