I have 10 participants randomly allocated to either a treatment or a control group and perform RNA-seq in pre and post treamtment (10 patients x 2 groups x 2 (pre & post)= 40 samples).

Based on example from section 3.5 of the edgeR vignettes, I used the following the design in edgeR:

~ Treatment + Treatment:Patient + Treatment:Cond

so my model in effect looks like this:

 [1] "(Intercept)"                      "TreatmentDrug"                   
 [3] "TreatmentControl:PatientSample10" "TreatmentDrug:PatientSample10"   
 [5] "TreatmentControl:PatientSample2"  "TreatmentDrug:PatientSample2"    
 [7] "TreatmentControl:PatientSample3"  "TreatmentDrug:PatientSample3"    
 [9] "TreatmentControl:PatientSample4"  "TreatmentDrug:PatientSample4"    
[11] "TreatmentControl:PatientSample5"  "TreatmentDrug:PatientSample5"    
[13] "TreatmentControl:PatientSample6"  "TreatmentDrug:PatientSample6"    
[15] "TreatmentControl:PatientSample7"  "TreatmentDrug:PatientSample7"    
[17] "TreatmentControl:PatientSample8"  "TreatmentDrug:PatientSample8"    
[19] "TreatmentControl:PatientSample9"  "TreatmentDrug:PatientSample9"    
[21] "TreatmentControl:CondPost"       "TreatmentDrug:CondPost" 

And I want to perform glmLRT(fit, coef="TreatmentDrug:CondPost") 

Now my question is,

1) aren't there too many parameters for the data I have? 

2) By asserting that model formula, am I making an assumption n-th patient in each group is the same?

3) If there is better way to model this, please let me know

1.) Yes. You appear to be miscounting. If you have 10 subjects, then that is 5 per group, each of which is measured twice, for a total of 20 observations, not 40. Also, you aren't following section 3.5 accurately. You want something like this:

Treatment <- factor(rep(c("Drug","Control"), each = 10))
Patient <- gl(5,2,length=20)
Cond <- factor(rep(c("Pre","Post"), 10))
data.frame(Treatment, Patient, Cond)
   Treatment Patient Cond
1       Drug       1  Pre
2       Drug       1 Post
3       Drug       2  Pre
4       Drug       2 Post
5       Drug       3  Pre
6       Drug       3 Post
7       Drug       4  Pre
8       Drug       4 Post
9       Drug       5  Pre
10      Drug       5 Post
11   Control       1  Pre
12   Control       1 Post
13   Control       2  Pre
14   Control       2 Post
15   Control       3  Pre
16   Control       3 Post
17   Control       4  Pre
18   Control       4 Post
19   Control       5  Pre
20   Control       5 Post

Cond <- relevel(Cond, "Pre") ## You probably want to relevel
design <- model.matrix(~Treatment + Treatment:Patient + Treatment:Cond)
> colnames(design)
 [1] "(Intercept)"               "TreatmentDrug"            
 [3] "TreatmentControl:Patient2" "TreatmentDrug:Patient2"   
 [5] "TreatmentControl:Patient3" "TreatmentDrug:Patient3"   
 [7] "TreatmentControl:Patient4" "TreatmentDrug:Patient4"   
 [9] "TreatmentControl:Patient5" "TreatmentDrug:Patient5"   
[11] "TreatmentControl:CondPost"  "TreatmentDrug:CondPost"  

## you can test if you have too many parameters  
> is.fullrank(design)
[1] TRUE

2.) No, you are controlling for the possibility that there might be patient-specific differences that you don't really care about, but want to account for, in case they exist. In other words, some of the patients might have higher or lower expression levels for a given gene as compared to the other patients, and you want to account for that, which may help improve your ability to detect drug-specific changes.

3.) Assuming you want to test both "TreatmentControl:CondPost" and "TreatmentDrug:CondPost", then this is what you want to do.