I am planning to go to UK from October 2018 to January 2019. My sister is already a UK resident and I will stay in her apartment. We agreed that I go there as early as October for me to experience autumn and to experience the Christmas holidays as well . I am already granted a visit visa that is valid until Feb 2019. My employer already approved my vacation. Is there a possibility that I will be questioned by the immigration officers due to my long stay in the UK? What documents do I need to provide to prove that I am a genuine tourist and will not overstay? Any feedback will be appreciated.
The most important question you need to ask yourself is not whether you will be questioned at the airport, but why jeopardize future UK visits by trying to game the system. In your comments you wrote:
what I included in my visa application is just one month because I believe they will refuse my visa had I indicated my 4 months stay.
Sometimes with visa applications, it is more important that you adhere to the spirit of the law than the letter of the law. You asked for one month, and end up spending four. That to me appears a material change. When you go back next time to renew your visa and the ECO notices, he can conclude you are not trustworthy.
In the fall of 1998 I similarly applied for a visa to visit the USA. It was my second trip. I requested 3 weeks and was approved with a one year visa, and given six months on my I-94 by immigration at the airport. I ended up staying five months and three weeks. Basically I followed the letter of the law, less than the six months I was allowed. I thought I was fine. The following year I applied for a new visa and I was denied the visa. The reason being the previous time although I did not overstay, I had stayed significantly longer than what I asked for. I violated the spirit of the system.
It appears you have not yet built an extensive travel history to affluent nations. This is not the time to try gaming the system because you have not accumulated enough international travel goodwill/history.
There's always a possibility you will be questioned by immigration. Things like where you come from, what you look like, the mood of the immigration officers a work that day, ... might all influence the decision of whether to pull you in for thorough questioning, but you'll always have to talk with them to actually obtain a leave to enter.
During this talk they will have access to everything the airline has told them (and much other information), so if they can see that you don't have a return ticket for anytime within the period your visa was granted for, that will raise suspicions. As they can probably also see that your previous application was refused, even a ticket that can be changed for a moderate fee might be enough to alert them, and staying privately does not count in your favour in that situation (if you were going to stay at a hotel, you would also need to extend that if you changed your ticket).
If you had a visa obtained rightfully and had travel plans in accordance with the application, I would think you were good. My advice would then be to bring (but only show if asked to) the documents you attached (or should have attached, like consent from your employer that you can go on a vacation for the duration) to your visa application (or a representative sample, i.e. if you attached 12 paychecks, bringing a couple is probably fine).
The problem here is that you have planned a trip significantly different from what you described in your visa application, that makes it possible to question whether the visa was obtained rightfully. And your travel plans are far from accordance with what was described in the visa application.
You run the risk of having the visa cancelled at the border (and as a result being denied entry) and get a note attached to your file that will make it harder to obtained a visa for the UK in the future. (Of course anything on the scale from being let in to this is possible)
The best thing to do is to contact the embassy (or consulate or ...) that issued you the visa, tell them that your plans changed significantly and hear what they say. And stop making dishonest applications for visas, if you get a visa (to anywhere) plan a trip accordingly.