Our company sends demo products to prospect whom would be potential clients.
The old procedure was to either by email or fax, send a copy of a
contract and its condition of aggreement have them sign and fax it
back. Then as per their request, our company makes an invoice of the
demos going, they would sign and fax that back. I would like this
process to be more efficient but have the same legal effect.

My question is. If I send an original email containing either the
terms of contract or invoice. That if they reply to this email, even
with no signature, they agree to the terms set forth.

Can this be used considering the factors that;
1. The reply comes back from them on their service.
2. Make specific they have to type a certain words on their reponse
   as an indication or as replacement for signature.
3. Make clear on the title and heading what this email is about.
4. Explain precaution to check the mail carefully, ex: select all to make sure
   theirs no other hidden text that they could see.

Can this be done? And in addition to the above, what other thing needs
to be added to the email to make it more legit in case of court
evidence?

http://www.biercekenerson.com/Articles/E-Contracts.htm

As a preliminary matter, I need to ask--are your e-mails CAN-SPAM compliant?

Assuming they are, this issue is really governed in contract law by
what is called the Statute of Frauds.  The SoF says that certain types
of contracts must be in writing so that there will be some indicia or
evidence of the parties' intent to be bound, rather than just one
party's verbal assurances that there was a contract.  The question you
raise is really one of whether an e-mail is a sufficient "writing" for
purposes of the Statute of Frauds.  A related question is whether an
e-mail, for evidentiary purposes, sufficiently manifests a meeting of
the minds as to the subject matter of the contract such that a court
could find that a contract was made.

For example, assume you e-mail a prospect a CAN-SPAM compliant
solicitation for widgets.  He e-mails back and says, "I accept your
offer to sell me 1,000 widgets for $15.99 USD, as evidenced by my
electronic signature hereinafter subscribed."  [Signed]  /john doe/ 
Then, if you printed that off and sent the widgets and if John Doe
protested and asserted no contract had been made in an effort to avoid
payment, you would adduce both the hard copy of the e-mail and proof
using subpoenaed records from his ISP that he actually got the e-mail
and actually sent the reply.  But you see the problem--and this is why
it's a Statute of Frauds issue--your customer can still assert that he
never replied to your e-mail, that his e-mail account was hijacked,
that he never got your e-mail to begin with, and so on.  It's all a
matter of proof and who the judge believes.  This is why paper
contracts with ink signatures are still the way to go.

Another example--assume that the customer is not contesting that he
replied, but he's arguing that there was never a meeting of the
minds--that your e-mail said "widgets" and he replied and said "I
accept, but I want blodgets."  If you ship him widgets and he refuses
to pay, he will argue that you never had a meeting of the minds as to
the subject matter of the contract and thus no contract was formed. 
Or what if part of your e-mail is cut off and the word "widgets" is no
where to be found and the guy accepts but he thinks he's getting
"gadgets"--same problem.

So I am not saying that an e-mail contract is not enforceable.  I am
not aware of any case law that says simply because a contract was made
via e-mail it is inherently invalid.  Indeed, the federal E-SIGN Act
says that you cannot invalidate a contract purely on the grounds that
it was electronically signed.  But the problem you will have is one of
PROOF.  If you are prepared to take as many steps as necessary to
evidence to a judge that the e-mail was CAN-SPAM compliant, that the
customer actually received it and actually responded and that there
was a meeting of the minds as to subject matter, you should be OK.