LINQ include and Projection

I have some classes defining entities with relationships

Account 
has many Conversations [IEnumerable<Conversation> Conversations]

Conversation 
has many Participants [IEnumerable<Account> Participants]
has many Messages [IEnumerable<Message> Messages]

Message 
has one Sender [Account Sender]
has one Conversation [Conversation Conversation]

I'm trying to write a LINQ query that returns a list of Conversation ordered by date and including related participants and messages.

public async Task<List<Conversation>> FindAllByAccountIdAsync(Int32 id)
{
    return await _Db.Conversations
         .Where(c => c.Participants.Any(p => p.AccountId == id))
         .Include(c => c.Participants)
         .Include(c => c.Messages)
         .ToListAsync();
}

This do the work but includes to much data i do not really need.

public async Task<List<Conversation>> FindAllByAccountIdAsync(Int32 id)
{
    return await _Db.Conversations
         .Where(c => c.Participants.Any(a => a.AccountId == id))
         .Include(c => c.Participants.Select(a=> new 
                       {
                          AccountId = a.AccountId,
                          Profile = new { FullName = a.Profile.FullName,
                                          Email = a.Profile.Email
                                        }                        
                       }))
         // Only return the last message in 
         // Eventually I would not return an array with a single object but just the single object inside associated with the property LastMessageIn
         .Include(c => c.Messages.OrderBy(m => m.Date).Select(m=> new 
                       {
                          Body = m.Body,
                          SenderId = m.Sender.AccountId
                       }).Last())
         .ToListAsync();
}

This script returns a mile long exception

{"message":"An error has occurred.","exceptionMessage":"The Include path expression must refer to a navigation property defined on the type. Use dotted paths for reference navigation properties and the Select operator for collection navigation properties........}

My mind resist understanding and learning LINQ I do not know if its just me but as soon requirements exceeds basic querying and projection it break out of my control

Someone have some hints?

I'm not sure if I understand your question, but I believe you want something like this:

public async Task<List<Conversation>> FindAllByAccountIdAsync(Int32 id)
{
    return await _Db.Conversations
         .Where(c => c.Participants.Any(p => p.AccountId == id))
         .Include(c => c.Participants)
         .Include(c => c.Messages)
         .Select(c => new 
         {
            Participants = c.Participants.Select(a=> new 
                       {
                          AccountId = a.AccountId,
                          Profile = new { FullName = a.Profile.FullName,
                                          Email = a.Profile.Email
                                        }                        
                       },
             //EDIT: using OrderByDescending and FirstOrDefault
             Messages = c.Messages.OrderByDescending(m => m.Date).Select(m=> new 
                       {
                          Body = m.Body,
                          SenderId = m.Sender.AccountId
                       }).FirstOrDefault())
             //others properties here
         }
         .ToListAsync();
}