More rules of thumb for you:
To digitize a pure sine wave and have the sequence of values *look* more-or-less look like a sine wave, it's often recommended to have a sample rate at least 10x the sine wave frequency with 20x being preferred.
So if you sample at 10 Hz, you can get a reasonable time-domain representation of a sine wave that's less than 1 Hz.
Your next problem may come from how you write your software to process your data and make decisions. If you're trying to characterize the *amplitude* of a sine wave, you'd better capture at least 1 full period of it, which requires a dataset representing at least 1 second. Whether you read that dataset all at once or whether you read a little at a time and accumulate, you need that >= 1 sec dataset to evaluate amplitude.
As to LV 2010, I'd venture that you're fine until that particular PC dies. I don't have the whole matrix of compatibility charts at my fingertips, but LV 2010 will constrain you to older versions of DAQmx which will in turn constrain you to older Windows OS versions and possibly older DAQ devices.
There are different pain points when trying to upgrade such old systems incrementally -- it's often better to do things all at once.
With a new PC, Windows OS, and LabVIEW version your LV 2010 code will likely convert pretty smoothly. Most often any DAQmx code will work out fine too if you are using a common DAQ device. You may be able to keep using the same device, especially if it's PCIe or USB.
-Kevin P
ALERT! LabVIEW's subscription-only policy coming to an end (finally!). Permanent license pricing remains WIP. Tread carefully.