There are lots of people sharing their experiences and helping out here. And I wouldn’t have been able to have such a great trip last month without them. So peruse and ask lots of questions.
I wrote a couple of posts based on your questions and information here that you might find helpful:
Florida Visitor Toll Pass
CLs
I don’t think Swan is a Monorail resort. Take bus to MK and ferry to Epcot and HS?
Swan is not a monorail resort. But you can actually walk or ferry to Epcot’s International Gate entrance and HS. There is no need to drive. That would help cut down on travel time. I would ferry, if you want to reduce the number of steps but that would depend on other factors when needing to get back and forth between the park and resort. The Swan and Dolphin hotels are the furthest from the park entrances at the Epcot Area Resorts.
And since you are at Swan, I would really reconsider needing a car for your entire stay.
Sorry if this is naive. Can I enter via International Gate Entrance or should I go by the regular entrance?
Not at all. That’s what we are here for.
One of the reasons people stay at the Epcot Area Resort is the convenience to get to Epcot through the International Gateway and HS by walking. The International Gateway puts you between the UK and France Pavilion. You just do your TPs based on that.
How should I commute to AK and MK?
I would go to MK by bus. If I had a car, going to AK by bus or car would depend on when the bus is arriving.
We really like the convenience (5 minutes from confirming for most rides to getting into Lyft and 10-15 minutes to anywhere at WDW) of Lyft last month but you need a car seat for your 5 year old.
Does Bus/Lyft drop at the park entrance which means less walk?
Bus and Lyft drop off are at the front of the parks. BUT Lyft for MK is at the T&T Center. We took Lyft to the Contemporary Resort and walked to MK.
which contemporary resort?
@vishnupriya_sureshbabu_719285 I highly recommend you considering picking up a copy of the 2020 Unofficial Guide to Walt Disney World by Bob Sehlinger & Len Telsa. Planning your first trip can sometimes feel overwhelming. This book breaks it down for first timers and pros alike.
https://theunofficialguides.com/product/the-unofficial-guide-walt-disney-world/
I bought the 2020 Disneyland version this year for my first time to the West Coast. I can’t recommend it enough!!
I need to book my stay for couple of days. Planning for Epcot and MK. Which hotel would you recommend?
Resorts are such a personal decision. Did you look into how much the Epcot Area and MK Area resorts cost? That may help you plan better.
If you are staying at the Swan, why aren’t you going to Epcot on those days?
Want to visit Epcot and MK for the second time.
https://touringplans.com/walt-disney-world/staying-onsite-or-offsite
“It may be less stressful to use the Disney transportation system, but with the single exception of commuting to the Magic Kingdom, the fastest, most efficient, and most flexible way to get around is usually a car.”
Is that true?
Yes. I always rented a car when I went to WDW for many years. The reason I no longer do it is because parking at the hotels is no longer free.
I use a ride share like Uber / Lyft now instead. They take you direct from your resort to the park for, usually, less than the cost of parking a car. Plus you don’t pay for renting. Lyft has saved me about $200 per trip.
I get mixed reviews transporting to MK. Some websites say it takes time as it involves commuting via monorail from parking lot. Keeping aside the cost part, which option saves time?
After reading the last few exchanges on this thread, I’m not sure you understand how Disney Transportation functions and what your options are. 
The monorail only stops at three resorts out of 25 and all three of them are the most expensive “Deluxe” resorts. The Contemporary Resort, The Grand Floridian Resort and the Polynesian Village Resort
So… before we go any further are you staying at The Swan as previously mentioned? If so, you will not be using the monorail at all to get to the parks.
I can go over all the ways to get to and from MK and the other parks, but it would save us both time if you at least give me an idea of where you might be staying.
Also, and I promise I don’t work for Touring Plans so I’m not trying to sell you anything, but I strongly believe you will benefit greatly from getting a copy of the Unofficial Guide to WDW. (If you don’t want to buy one maybe see if your local library has a copy of an previous years version. Each year is, basically the same with info added about the newest stuff. However, they always go over the basics of a WDW vacation in each edition.)
At the very least, go to YouTube and look at the Touring Plans channel. They have a great selection of videos that will answer a lot of your questions.