Hi Olivier, thank you for reaching out. All of our websites have an automatically generated SSL certificate which makes the website secure. If you reach out ot us via live chat or at support@bookmark.com and send us the website name and your account email we can review further if you are having issues. 
You can add your logo if you head over to Design->Brand and you can add an image there and make it so every time a customer clicks on the logo they are taken to the home-page. Please bear in mind that if this option is turned on this will be the case for all pages you have not just the home-page. For detailed instructions please review the following article: https://help.bookmark.com/en/articles/5683413-how-to-change-your-brand-and-logo
In order for you to disable the code in the form submissions, you will need to turn off the google captcha. To do this navigate to Site->General Settings->Google Captcha and toggle the Show Captcha button to off. 
Feel free to reach out to us on live chat if you need further information or assistance.