Hi Camilla,
As per my understanding, you should first iterate over all related membership of contact person, conditional statement will be nested in each loop.
e.g: I created a custom entity "Membership" and 3 demo records and changed my publisher prefix to cgi as yours.

Dynamic expression in marketing email:

As doc stated, operator(eq) is not required for boolean field.

So the conditional statement will be: {{#if this.cgi_roadassistance }}, it is equivalent to true,
and the whole expression is:
Hi {{contact.firstname}},
{{#each contact.cgi_membership_contact_new_contact}}
{{#if this.cgi_roadassistance }}
{{this.cgi_name}}, Road assitance is available.
{{else}}
{{this.cgi_name}}, Road assitance is not available.
{{/if}}
{{/each}}
Preview result:

To apply it to your requirement, you might need to edit HTML code directly to add image element.(e.g: <img src="xxxx" width="100" height="100">)
Just add the element inside {{#if}}{{/if}} body.
Regards,
Clofly