When using telephoto lens, usually what is the setting to use?

When I use my 75-300mm lens, I usually set at faster speed such as 1/250 or else the picture will not be sharp ( hand shake effect). I went to take some photo of fashion show at outdoor in sunny whether under tentage. The lighting condition is good,but I still used flash. When I went back to download to my notebook, I am gald that I did as those photo I took without flash turned out a bit under expo.I added +1/3 and +2/3 flash exposure compensation to brighthen up the skin complexion of the models.The photo turned out ok. However, some appeared a bit of over expo and the skin complexions are a bit greyish. By the way as I am using notebook to view, wondering it able to give more accurate colour, as ever heard people comment to use tube type of monitor is the best for viewing and do editing for photo? When I studied the histogram, I realised that the the graph is normal except at the right side, ( about 3/4 from the left, 1/4 from the right side, it shoot up at the way.) Base on my setting below, is there any wrong?

Shooting Mode Manual Exposure
Tv( Shutter Speed ) 1/250
Av( Aperture Value ) 4.5
Metering Mode Spot Metering
ISO Speed 100
Lens EF75-300mm f/4-5.6 USM
Focal Length 110.0 mm
Image Size 3504x2336
Image Quality Fine
Flash On
Flash Type External E-TTL
Flash Exposure Compensation +2/3
Red-eye Reduction On
Shutter curtain sync 1st-curtain sync
White Balance Mode Auto
AF Mode One-Shot AF
Picture Style Standard
Sharpness 3
Contrast 0
Saturation 0
Color tone 0
Color Space sRGB
Noise Reduction Off

Now that my flash is not working, I am wondering what setting to use for the outdoor shoot to prevent hand shake effect and under/over expo, as there will be another round of fashion this weekend and don't think enough time for me to send my flash for repair. Sometimes at outdoor, even when opening the apexture to maximum and speed to about 1/125, the camera was detecting under exposure. By the way if the speed is reduced to 1/125 and when zoom to maximum, definitely there is be hand shaking effect. Will using monopod helps? But I don't have it at the moment The next thing come to my mind is to push up the ISO speed, will that is lead to digital noises??