is it true that branded pc work faster then assembled

Well it is not 100% true but almost always that actually is the case that branded computers are faaster than others. Assembled Computers are assembeled by Computer Hardware engineers, but they never check compability and stuff like that. But hp since it is a huge company and they'll make a lot of similar systems so they put together computer peripherals that are 100% compatible to the motherboard and processor. So in such cases the assembled computers donot function as well as the branded ones.

I don't believe so, i think the problem with your PC is the celeron processor which is the low end of Intel Pentium product. That's never go for computer running on celeron processor. It's very slow compare to the normal pentium

For the same specs of DIY and branded computers, the only advantage I see of the later is it reliability. Branded computers has a name to protect so they ensure that all parts are perfectly match hence a very small if any speed advantage. For the same price a properly customized DIY can easily beat a branded one, because we can channel the cost where we need it and the price of royalties can be spend on the extra feature. This is only true if its properly designed.

Assembled computers may not be optimized for the performance. While the branded computers are optimised for performance. I strongly believe in favor of use of branded computers. Though initial costs are higher but the costs justify the value for money.