a. If I am based in Texas and selling within Texas, I should charge my Customers Origin-Based Sales Tax which would be: Texas Sales Tax (6.25%) + My City Tax (2.0%) making it 8.25%. Is that right?
b. If I am only based in Texas and no relation in other states (Sales Tax Nexus), do I charge sales tax to my customers in other states?
c. Also if supplier is located in e.g. New Jersey and client is also in New Jersey then supplier will charge us tax but we are not charging any tax to customer because we are located in Texas then will that tax amount paid by us will be considered as cost?

I think you are confused about all of it, and it all depends on how the supplier operates.
Are you going to be using this 'supplier' as a dropshipper (they provide the goods and ship to your customers)?
A business who is charging sales tax to the end buyer does not pay sales tax to it's supplier.
You provide your tax ID (given to you by your state) to the supplier.

BUT do not confuse that with using a supplier who remits the BUYER'S taxes to various states (plus TX), as part of your agreement.

IF YOU are in charge of remitting taxes:
You charge sales tax to whichever states the supplier has an entity in, often warehouses in several states.
You need to know what tax is owed for each state.

IF THEY remit the taxes:
You collect it and remit it to the supplier, and they remit it to each state.

As for local sales, you collect the state tax for the whole state, but the city tax for only customers in your city. That includes all walk ins, and all shipments to your zip code or codes.

The sales tax landscape is constantly changing, as there is more online selling and states are missing out on revenues. I don't know the latest laws. I do experience frustration with nuances all the time - e.g., my state doesn't charge tax on food, but online sellers who use suppliers with an entity in my state insist on charging tax anyway. I think they can't be bothered to write software with details of exemptions for all the states they are in.

You need to carefully examine the contract with your supplier.
And be very, very wary of suppliers, many of whom are not legit.
Your first caution should be asking yourself Why aren't they selling their goods to the end users for the real profits, instead of to resellers?

Thank you so much joypulv for your response. Here are some more explanations what I needed to ask.

Are you going to be using this 'supplier' as a drop-shipper (they provide the goods and ship to your customers)? [Saad] YES

A business who is charging sales tax to the end buyer does not pay sales tax to it's supplier. [Saad] Agreed, I dont.

You provide your tax ID (given to you by your state) to the supplier. [Saad] Agreed, I do same.

BUT do not confuse that with using a supplier who remits the BUYER'S taxes to various states (plus TX), as part of your agreement.

IF YOU are in charge of remitting taxes:
You charge sales tax to whichever states the supplier has an entity in, often warehouses in several states.
You need to know what tax is owed for each state.


IF THEY remit the taxes:
You collect it and remit it to the supplier, and they remit it to each state.

[Saad] By looking at above of your explanation, when my SUPPLIER is drop shipping to an end customer who is in same state of SUPPLIER or his WAREHOUSE then either SUPPLIER can remit the Sales Taxes to that state or I can.

So my initial question where MY SUPPLIER is sending good from NJ to NJ and charging Sales Tax on invoice to me, I have to charge same from my Customer.

Why it was trouble for me is, Customer bought 10 items from me which I was able to arrange from 4 different suppliers 3 of those doesn't exists in NJ and didn't change Sales Tax but 1 has Warehouse in NJ charged me Sales Tax for that drop-ship.

I should charge my customer sales tax for 2 of 10 items here which were sent to them from within NJ.