Currently, I have the following RNA samples and want to see any up/down-regulated gene expression in proband to explain the disease-causing of the proband.

Sample1: (Proband) blood
Sample2: (Proband) fibroblast 
Sample3: (Control person #1) blood
Sample4: (Control person #1) fibroblast 
Sample5: (Control person #2) blood
Sample6: (Control person #2) fibroblast 
Sample7: (Control person #3) blood
Sample8: (Control person #3) fibroblast 

In this case,
1. Can I do the DEG? Any tool would be better in this case (DESeq/edgeR)
2. Can I treat control samples as biological replica of proband? If not, I know edgeR has a section to deal with the case without replica
3. Is it statistically significant? And any way to improve in a better setting?

Thanks a lot!

My advice would be to analyse the blood samples and the fibroblast samples separately. Then the comparison of the proband with the control samples is a simple two-group comparison (n=1 proband vs n=3 controls). Any of the usual packages limma, edgeR or DESeq2 would be able to do the DE analysis easily.