Is Http Trigger execute all request in parallel or sequentially or there is any limit for parallel threads in Http Trigger.
It should be paralleled executed, in your case it seems that there is no enough resource for dealling with the request in your service plan.
For Azure function there are 2 different modes: Consumption plan and Azure App Service plan. We may could get more info from Azure document.
The Consumption plan automatically allocates compute power when your code is running, scales out as necessary to handle load, and then scales down when code is not running.
In the App Service plan, your function apps run on dedicated VMs on Basic, Standard, and Premium SKUs, similar to Web Apps. Dedicated VMs are allocated to your App Service apps, which means the functions host is always running.
It seems that you are using App service plan, if it is that case, please have a try scale up or scale out your service plan.