You can use a simple series resistor to attenuate the input signal to the counter. If the counter has 50Ω input impedance, putting another 50Ω in series with the input will attenuate the signal by 2 (the series resistor and the input impedance form a
resistive voltage divider). For more or less attenuation chose another series resistor.
Any counter will operate more reliable when provides with a square waveform. Internally any waveform is converted to a digital signal (square wave) anyway for processing by the counter's logic. This is done by a comparator circuit (usually with adjustable threshold). A sine waveform crosses the threshold of the counter comparatively slowly.
Add some noise and you'll have multiple pulses near the threshold instead of one single pulse (by "add some noise" i do not mean that you have to add noise intentionally, any noise, hum etc. picked up by your setup will have this effect).
At higher frequencies this effect is less seen because the sine signal crosses the threshold faster and there is less time for noise to create additional pulses.
Your counter may (or may not) have a filter that can be switched into the signal chain to reduce high frequency noise somewhat.
A counter is typically more accurate than an oscilloscope. You can read the period of a signal from an analog oscilloscope. The accuracy is limited by the accuracy of the timebase which in an anlog scope may be 3% or so. A digital oscilloscope may offer higher accuracy and often can display the frequency directly, but is limited to teh resolution of the sampling circuit. A counter is an instrument dedicated to counting (or measuring frequency) and is therefore optimized to minimize these problems.
For low frequencies I'd recommend not to measure the frequency at all. Measuring a frequency means counting the number of signal changes within a fixed period of time (e.g. 1 second). A low frequency signal doesn't change very often within a second. As a worst case example consider a 2Hz signal and acounter counting for 1second. Depending on the moment in time you start counting, you may see 1 or 2 pulses within that one second. Your display will be highly unstable. You'd have to measure much longer for good resolution.
Typically you measure the period of a low frequency signal instead. A counter normally has a period measurement setting. The roles of signal and gating (gating sets the time for measurement, imagine a gate that lets the signal pass only while it is open) are reversed: The counter generates an internal, precise timing signal at high frequency. The signal is used to control the gate for this high frequency reference clock. The number of pulses counted within one period of the input signal is a direct measure of the time of that period. You get frequency from f=1/T.
A single shot does not have a frequency. The frequency is a measure of the number of times a signal repeats within one second (that is why the unit of frequency is 1Hz=1/s). A signle shot doesn't repeat and therefore has no frequency. You can, however, measure the duration (not period, becasu a signle shot is not periodic) of a single shot event.
P.S.: This seems to be about the 3rd thread you opened concerning counters. Please stay within one thread. This is easier for others to follow and give advice as well as it is easier for you than to match replies from different threads.