There is nothing wrong with a man greeting a non-Mahram woman with Salam, without shaking her hand, if she is elderly. However, he should not greet a young woman with Salam when there is no guarantee that there will be no Fitnah (temptation).

1. There is nothing wrong with the person who is initiating the greeting saying, “Salamun `alaykum” or `Salamun `alayka.” Allah tells us that the greeting of the angels to the people of Paradise will be “Salamun `alaykum”. 2. Is it disliked to initiate the greeting by saying ‘`Alayka As-Salam’ or ‘`Alaykum As-Salam,’ because this is the greeting given to the dead. 3. The most complete form of greeting is to say ‘As-Salamu `alaykum wa rahmatu-Allahi wa barakatuhu’ or ‘Salamun `alaykum wa rahmatu-Allahi wa barakatuhu.’

• If the house is not your house, and you want to enter it, then you must ask permission. • If the house is your house, and no one else is living in it, then you may enter without asking anyone for permission. • Seeking permission to enter someone’s house is waived when: 1- it is not possible to give permission; 2- asking permission could result in harm; 3- for the one who has a right and asking for permission will cause his right to be lost. • Praising other people which means speaking highly of someone for some good that he did, or for some good characteristics that he possesses is permissible in Islam.

• The best and most complete phrase to use when giving the greeting of Salam is: “As-salamu `alaykum wa rahmatullahi wa barakatuhu” and the best phrase to use when returning the greeting is: “Wa `alaykum As-salam wa rahmatullahi wa barakatuhu.” • With regard to adding ‘wa maghfiratuhu’, it is mentioned in some Hadiths with regard to initiating the greeting and returning it, but these reports are not sound.

The wording of the response to the greeting mentioned is acceptable, even though it is better to use the complete form when returning the greeting, based on what has been explained in the long answer.

With regard to du’a for entering the house, one should mention the name of Allah, remember Allah and give the greeting of salaam, even if there is no one in the house. For more, please see the detailed answer.

Conclusion: there is nothing wrong with you joining the sports club as mentioned in the question, and what you have mentioned about matters concerning which there are reservations can be avoided easily, praise be to Allah. And Allah knows best.

To sum up all of the above: prostration to anyone other than Allah does not constitute disbelief unless it is done by way of worship. But if it is done by way of greeting, it is a major sin but it is not disbelief.  And Allah knows best.