UK visitor Visa financial query

I am new to this community and my question might seem bit not specific or repeated (though I didn't find proper answer for this upon searching the site) and open-ended but any kind of input or suggestion is well appreciated.

I am an Indian national, 28 years old and finished my Masters in 2015 (still unemployed)

I am applying for UK visitor visa to check universities' departments and meet few professors to consider for PhD program.

Sponsor -- A family friend of mine who is a British-Indian, is sponsoring entirely for my trip of 10 days.

My personal bank account -- rarely used but 2 months ago, my father deposited about 15 lacs ( roughly 17,000 pounds) after sale of a property which is there untouched from last 2 months. I have all the required documents of property sale and transaction related to the property sale etc.

Supporting documents - I have agricultural lands and some another properties on my name which I intend to show in my application and I do have some travel history around few Asian countries.

My father wont be in India for another 3-4 months due to his work trip. So, I am unable to provide any of his Bank documents.

my query is - though this trip is costing me nothing ( as being sponsored by family friend), is it still mandatory to provide my father's bank statements?

my personal bank account has above mentioned balance for last 2 months ( I have sufficient proof of where the money came from) but before that it was pretty much inactive and low balance of about few hundred pounds, will that be a problem?

Being sponsored for the trip, still need to show 6 months bank statement?