Although inspection is a personal thing (I know people in the hive weekly and some who rarely pull a cover) but ideally since the nectar and pollen seasons are in reality NOT all that long - I suggest LOOKING inside the hive AT LEAST once every two weeks, but paying attention at the entrance and watching your bees in flights is somethng that MOST PEOPLE can do more often - unless of course the bees are kept off-property.
Feeding is a NOW thing for you and me - cooler days (compared to cold days) cause the bees to be more active (although not neccessarilly outside the hive) so the consume the honey they have store in the corners and other random places that CLUSTERS have tougher times getting at.
Your food source can fall dramatically in a cool Spring if y our bees are only flying an hour or two a day.
Feeding them using an in-hive (top feeder) offers them the LONGEST feed cycle - that is an inverted feeder jar on top of the inner cover opening. But even an entrance feeder will attract workers as the temperatures allow and the only real advantage is that you can easily see the sugar water go down in the jars at the entrance.
The bad side of an entrance feeder now is robbing by ants typically, but I have used entrance feeders all times of the year and rarely had a problem worth mentioning. It is JUST something to keep in mind.
So feed NOW!!!!! Inspect at least every other week!!!! That is what I would tell any new beekeeper that is asking me in person for mentoring. Honestly though, if the time allows - I'd be in the hive ONCE a week and always trying to think one step ahead of the bees - they can be CRAFTY little buggers
Hope that helps.
PS.... although you read all kinds of mixtures - I use 1 gallon of hot water with a 5 pound bag of sugar melted slowly in it, and then cooled to ambient temps as Sugar-Water. You can adjust that up or down, thicker or thinner - but I find it is accepted well and does not crystalize up on me onces stored.