Using a multimeter, can I tell if a lithium-ion battery pack is brand-new?
Whether a battery is brand new should be detectable from quality of housing and printed datacode. However, determining if a battery is "brand new" in not a very useful parameter. Manufacturers of smartphones/tablets can use different sources for Li-Ion batteries, and after-market batteries may have a different (even a bigger) "rated" capacity than the original battery. However, actual capacity of Li-Ion batteries varies depending on charge-discharge rate, and battery temperature. So the results of measurements might disappoint.

Regarding the question (1), no, according to Battery University article, BU-902: How to Measure Internal Resistance, the DC battery impedance is not a very good indicator of battery SOH - State of Health. The impedance would go down significantly when the battery is really EOL. Regarding how much the internal resistance varies from one battery of about same size, yes, it differs for "low discharge" batteries as compared to "high-discharge" batteries, this is one of design parameters.

The same article also explains how to measure internal resistance of a battery. Your idea of measuring it with DMM in Ohmmeter mode is absolutely wrong. The article also explains that the battery equivalent model has more than one impedance, depending of load frequency you will get different results. The simplest approach is to measure the lump DC impedance, but it is a poor indicator of battery health.

Finally, no, you can't tell if the battery is good with simple DMM measurement. The only right approach is to measure the actual battery capacity under conditions specified by manufacturer, using approaches as explained in the linked SE answer. And then compare the result with either advertised capacity, or to batteries with similar size and construction. A load of information about actual performance of batteries can be found on this website, lygte-info.com