The key question here is whether the Entry Clearance Officer (ECO) examining your application will determine that your marriage is a marriage of convenience. The UK has produced far more specific guidance on the topic of marriages of convenience than existed the last time I looked into this. The current guidance is also much more flexible than the previous guidance. For example, it no longer categorically excludes couples with children from suspicion of a marriage of convenience, nor couples who have cohabited.
Would it help to show our relationship via WhatsApp messages, Wedding photos, Dating photos etc?
Yes, you should do that. The current guidance (linked above) is redacted; the factors that allow an officer to suspect a marriage of convenience are not disclosed. Older guidance, however, included a threshold of two years. That is, a couple whose relationship is less than two years old could be suspected of a marriage of convenience. You should therefore assume that you will have to overcome such a suspicion.
If the ECO does invoke such a suspicion, it remains the burden of the ECO to prove that yours is a marriage of convenience. That is, they're not supposed to refuse the application simply because it lacks wedding photographs. In practice, though, it seems they often do. You should therefore include evidence that your relationship is genuine.
In addition to messages and photographs, you should include, if you have it, evidence of the time you have spent in each other's physical presence. For example, if you live together, include the lease if you are both named on it, or utility bills, or official correspondence addressed to your shared address. You may also want to include train or plane tickets for travel you have undertaken together. If you have a joint bank account, consider including an account statement to prove that you are combining your finances. Any evidence that involves a third party (a government body, an airline, and so on) will be stronger than evidence that does not. The strength of the evidence will depend in part on the third party: a government is better than a company; a company is better than a person; an unrelated person is better than a friend or relative.
But don't overdo it, lest you overwhelm the ECO. If you have a joint bank statement, for example, including evidence of your joint gym membership would probably not add anything, and may hurt your application. Providing unnecessary evidence can work against you in two ways: First, it makes it harder for the people reading your application to find the information they really need. Second, the more information they have, the more likely they are to see inconsistencies in the application.
You should also, of course, pay attention to the information on the page Documents you must provide.
Would it help to provide all my educational qualifications? I am in IT and have a number of certificates and diplomas (idea is to show I will not be burden on the state).
No, that is not necessary. There is no test of whether an EEA family permit applicant is likely to become a burden on the state.
Because the EEA family permit application is free of charge, I would advise you not to worry too much about it. Present the best application you can, and if it is refused, pay careful attention to the points mentioned in the refusal letter. Then submit a second application that addresses these points.