Which Facebook post has got maximum likes and shared maximum number of times?

There is no way to find that number in an exact way. I do not think there are any tools available to find the maximum number of likes received by a single Facebook post.

However, records indicate that the post created by Lady Gaga on the Thanksgiving Day in December 2010 has garnered a total number of 83769 likes.

In 2015, a post with a child carrying a sign with a message to beat cancer got more than 10 million likes. It also received thousands of shares. You can check the post at the link https://www.facebook.com/Im1Israel/photos/a.180548791981836.33384.178454358857946/851019981601377/?type=3

Content by celebrities exceeds the limits most of the times. So do the messages with a social cause. London Evening Standard post about Champagne preventing Alzheimer disease got a total of 938000 shares in 2015.
A post to a link to an article on Huffington post about the addiction and the causes got a whopping 2 million shares last year. The Facebook post went quite viral.

The top shared posts in 2015 were

1. Kim Davis

Kentucky County clerk Kim Davis who was arrested for disobeying the law permitting the same sex marriage was released. When she was released, the news went viral. It garnered a total of 489606 shares.

2. President Obama

President Obama's thanksgiving dinner to Washington DC homeless was shared 298193 views.

There are too many variables which makes it impossible to find out post with maximum likes and shares. However most of the time readwriteweb, mashable and boingboing report about specific posts going viral under headline "internet is broken due to". However in reality a lot of controversial posts also get deleted or the person gets banned despite getting large number of shares. And that makes it harder for other social media monitoring companies to keep tab on such data.

Some of the instances where posts have gone viral. A person from New york shared his inbox conversation with his girlfriend cheating on him went viral with 185,215,734 shares. This post was shared on lot of pages across the world and groups. It was removed after 36 hours of being viral. The account of the person was removed too. That post got the maximum likes and shares but Facebook policy violated in this context so the person account was removed.

Similarly you can check accounts of Dan bilzerian, superwoman, nicole arbour to see how their posts are going viral in larger numbers.

Accounts getting closed, post removal and private sharing of post stops the actual data of shares and likes being miscalculated. Especially private group sharing or private share among friends doesn't get recorded in the list of shares. This is the reason a lot of data remains miscalculated.