For various ranges of "parameters", I routinely generate the same quantity of
random numbers using the Data Analysis, Random Number Generation function
("uniform" distribution).

Because I need to be be able to reproduce the random numbers, I choose a
"Random Seed" number.

My observations/questions are as follows:

Are the random numbers returned for a certain seed number indeed random
according to a uniform distribution? Are the "seed-related" random numbers
any less random than random numbers returned without using a seed number? I
ask because there appears to be a linear pattern with the first random number
returned for seeds 1, 2, 3, 4, etc., for a specified range of parameters.

Is there a range of seed numbers that one must stay within when choosing
random numbers from a specific range of parameters. For example, for
parameters 1 to 1,000, must one choose a seed number from 1 to 1,000?

In general, are there any guidelines/limitations inherent with Excel that I
should keep in mind when assigning a seed number? Also, is there a
"standard" random number generator that practicing scientists and engineers
typically use other than Excel?

Thanks for any assistance you can provide.......