I would still ask for the returned counter-signed contract Rows, just in case.
As for using your name and reputation, they cannot include your company name in any of their tender submissions unless you have expressly permitted them - If they refuse to pay you and/or do not return a signed contract, but have used your details in their bid, they are acting unjustly imo.
You might want to see if you can view their submissions if there is a planning portal? (depending if it a government tender or not) to see if they have already used your details as part of their bid?
I would think that if they have gone silent, they may have missed the deadline on the submission or perhaps have lost interest in the bid - I don't think they would ask you to help, then submit the bid without contacting you - they obviously need you to assist first or they wouldn't have approached you.
Try contacting them again to see were things lie, and if they have decided not to proceed, stay civil - you might be offered something more concrete with them in the future - a larger tender perhaps.
All the best, Peas.