No security clearance with 5 year residency for officers role in Infantry/armoured/parachute right?

Are you eligible to apply, Yes. Is the application window open for any Commonwealth country, no. Due to an unprecedented number of applications from Commonwealth nations unfortunately the window has temporarily closed.

SC will be gained as part of the application process.

Alright and if I join as a soldier in future and after completing my training, within how many months can I apply for officer selection as I already have a degree in mathematics?

Yes, you can join as a Soldier and then commission. Some do it, personally I'd recommend joining straight as an Officer is that is the aim. Whilst it used to be impressive to have a degree, most people both Soldiers and Officers tend to have them nowadays.

Earlier I talked about 5 year UK residency for security clearance for officer roles in Infantry/Armoured/Artillery etc. You had replied that yes I am eligible, I forgot to tell you one thing that I have never lived in UK so how will security checks be done?

Ah, apologies and thanks for the quick response. I interpreted it as though you had 5 years residency.

In that case, whilst we recruit from Commonwealth Countries the portal to do so is currently closed, nor are we informed as to when it will reopen. All i can suggest is refer back to the website and see when the Commonwealth portal reopens or gain a visa to the UK and remain for several years to be eligible.

Nationality And Commonwealth | How To Join

Security clearance needs 5 year UK residency for non sensitive officers roles also? Can't it be done through my home country's documents.  

In November 2018, 5 year UK residency was removed for commonwealth citizens except for sensitive roles like intelligenc etc.

You are absolutely correct. However, the portal that receives applications from such countries has been closed for quite some time. The window to apply is so small due to the high application rate. As frustrating as it may be, all i can suggest is to refer back to the website daily to ensure you are made aware the day it reopens.

If someone already has a degree and joined as a soldier and now wants to go for officer role, approx after how many months of service the person can talk to chain of command about applying for AOSB?

If you were to join as a Soldier then it would depend entirely on the individual and their Chain of command as you'll need to be endorsed the recommendation to attempt AOSB.