Shipping:
Many of us use EPS or CPS here, it's stupid simple and as Chip pointed out, any package with a value under US$200 comes in tax free.
You sign up with EPS or CPS and they give you a postal and shipping address in Miami.
You have the goods shipped to Miami and they ship them here.
EPS allows you to track your packages online and see all the charges before you pick the package up. Right now they charge around RD$190 per pound to ship from Miami to the DR.
When I order something off Amazon, it's in my hands within 7-10 days.
I have shipped maybe 40-50 packages and never had a problem.
Electronic goods, books, spare parts, food items etc.
Internet:
The fastest you can get is a 5MB ADSL from Codetel.
Will run you around US$200 monthly.
They are by far the most reliable provider here, I have tried them all.
See the pricing at the link below:
Codetel ADSL Pricing
What connection you can get is location dependent.
If you want to get round the IP blocks in the USA etc.
Lots of VPN options so you can watch and stream movies, ABC, ESPN etc.
Power:
The is location dependent. e.g. If you live in Punta Cana, the power is VERY reliable and they almost never have any sort of blackout.
The better apartment buildings in the country have generators. You can also by and inverter and batteries that will give you power.
Power reliability comes down to many factors. What part of the DR do you want to live in? How much do you want to spend? How critical is your need for 24x7 power?
I would take a good look around the forums and use the search function.
Your questions have been answered in-depth many times on DR1.