Number of recommendations here:
The colleague assigned for helping me out is deliberately delaying in providing information and has very good ties with everyone in the company
First up, completely remove this type of thinking, because whether you are aware of it or not, this thinking will affect your behavior to said co-workers, which will then affect their interaction with you. It is the kiss of death to working relationships.
My manager who earlier friendly is now avoiding me and has become cold to me ... A few hours later, I see the task being completed by him
Seems to be an assumption that the delaying co-worker is talking to the manager and serving diss. Could be, but why jump to that conclusion? It will only affect how you work going forward.
I have been in the situation of helping a new dev a number of times. The one thing which made a difference in the interaction to me was the effort they put into something before contacting me.
E.G. did they write a lot of code and have bugs they can't figure out? - versus - they have little to no code asking what to do. Did they read the document given them and have specific questions on that document/instruction, or did they skim it or not read at all and then ask what to do?
Have no background on your tasks and your efforts on them, so not saying you are doing this, but just something to keep in mind. Put in a solid attempt before requesting help with something. Don't try to get help with everything.
You have just under half the probation time left. Recommend forgetting all the 'politics' stuff and get down to task at hand: put your own time into studying what you need to be able to complete your tasks.
Talk to the manager just as @Benjamin outlines, and then over the next 40 days, work hard, study, focus and you can start to hit your deadlines. The early 50 days would be considered a learning curve struggle, if you have it down by 90.