Is ‘constructor LocationRequest()’ deprecated in google maps v2?

Yes, the LocationRequest constructor is deprecated. You can use its static method LocationRequest.create() to create a location request.

Kotlin:

locationRequest = LocationRequest.create().apply {
    interval = 100
    fastestInterval = 50
    priority = LocationRequest.PRIORITY_HIGH_ACCURACY
    maxWaitTime = 100
}

Java:

locationRequest = LocationRequest.create()
    .setInterval(100)
    .setFastestInterval(3000) 
    .setPriority(LocationRequest.PRIORITY_HIGH_ACCURACY)
    .setMaxWaitTime(100);

Update

As @Shimon pointed out LocationRequest.PRIORITY_HIGH_ACCURACY is now deprecated, so instead use
Priority.PRIORITY_HIGH_ACCURACY