Thank you for reaching out! It's absolutely fine for you to send an email on behalf of your colleague while they are away on a business trip. However, before sending the email, make sure you have their permission and access to their email account.
Regarding the photo you mentioned, it would be helpful if you could provide more details about the content and purpose of the photo. Depending on the context, it may or may not be appropriate to send it in an email. If the photo is relevant to the discussion or adds value to the communication with the Egyptian client, then it should be fine to include it. Just make sure that the photo is professional and in line with your company's image.
As for the addressing, the best practice is to use a formal and respectful tone when referring to the client. It is advisable to address them by their last name, followed by a polite salutation like "Mr." or "Ms." For example, if their name is Ahmed, you can address them as "Mr. Ahmed." If you are unsure about the proper form of address, you can use "Dear Sir/Madam."
I hope this helps. If you have any further questions, feel free to ask.