Is it possible that the small yellow balls in the soil could be fertilizer? We don't know if new plants or soil were recently added.
It is most likely a fungus (mushrooms). Here is more information: https://www.gardeningknowhow.com/houseplants/hpgen/getting-rid-of-mushrooms-growing-in-houseplant-soil.htm
My soil is small grained and does not form a ball. What type of soil is this?
I think I saw it's bead like. Do you work it into the soil? How deep? Does it come as a liquid and you spray it into ground?
There are a number of ways to add nitrogen to the soil. This article will tell you more: https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/nitrogen-plant-fertilizer.htm
I have seen few videos in which they say you should add compost to your clay soil but nothing about potting soil. So which one shall I add potting soil or compost? Thanks
In the US, compost means only decomposed organic matter -- if you are trying to amend outdoor garden soil, that is what you want.
Suggestions for adding lime?
The simplest way to sweeten soil organically is to add organic material - peat, compost, etc. Here are a couple of article you might find interesting: https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/lower-acid-soil.htm
Info on using activated EM to change soil pH level.
You might find this article interesting: http://www.motherearthnews.com/organic-gardening/making-biochar-improve-soil-zmaz09fmzraw.aspx
Which crop would you recommend for the soil with 9. 7 phosphorus?
Not much will grow in that soil. You should build a raised bed with some really good soil , and overtime keep mixing some lower Phosphorus soil into the area you want to eventually grow stuff in.