Allahabad - Varanasi - Ayodhya Bus facility

We are planning for a trip to the following places.

Day 1: Arrive to Allabad from haridwar @ 8 a.m. Visit imp. places in Allahabd & after lunch proceed to Varansi by Bus. Reach Varanasi & see the Ganga Aarti.
Day 2: This will be on Friday. Leave Varanasi around 4-5 p.m by bus & reach Ayodya @nigh & stay.
Day 3: Early morning visit Ram Janmabhoomi & proceed to Lucknow by bus & from there visit Naimisharanya & back to Lucknw & catch the train to Mathura @11.55 p.m.
Day 4: Reach Mathura & visit the imp. temples @ Mathura, Brindavan, Gokula & Govardhan & proceed to Delhi to took a flight @ 8 p.m to Bangalore.

I want the suggestions for the foll.
Kindly let me know whether can we get buses from
1. Allahabad to Varanasi in the afternoon.
2. Varanasi to Ayodhya around 4-5 p.m & travel time.
3. Ayodhya to Lucknow @ 9 a.m & what is the travel time

we are planning to hire a taxi from Lucknow-Naimisharaya-Lucknow
as we have not much time. whether 7 hrs will be enough for this ?

Is it possible to see imp. temples @ Mathura, Brindavan, Gokula & Govardhan in 5-6 hrs. & planning to hire a taxi to Delhi from Mahtura. let me know the travel time from Mahura - Delhi Airport by taxi.

Others will have better ideas about Ayodhya and Lucknow, but you can easily find buses from Allahabad to Varanasi at any time of the day and even late at night. State Transport (ST) buses to Varanasi leave from the Civil Lines Bus Stand.

Is it necessary to take permission to visit Patalpuri temple & Akshaya Vata in advance ? if u have the contact no. of Ordnance Depot.pl. mail it.& will half a day is sufficient to see the imp. places @Allahabad ?