Believe me I am no expert but, am still growing the same plant we bought for our house when we lived before the house we have now, so were talking 38 years. The plant you have shown in the picture is definitely the Swiss Cheese plant common name here in UK is (Philodendron )Monsteria, some of the leaves have not got all the cut and holes in them BUT, this is because your plant is classed as immature and the sign of maturity is when the leaves begin to open out with the cut and holes that are beginning to show on your plant, as the year / years go by, every leaf will have the Cut / holes in them.
The plant I have has been cut down so severely no one expected it to regrow, I left about 3 leaves on the stem, but it grew like Topsy and was so healthy I cut the rest of the stems up and replanted them and they rooted into nice fresh compost, so my friends all have off cuts from my plants.
Some only lasted a few years as you were informed but others have grown so large they have been re-housed at other friends who have the space.
As for care, ALL these plants no matter the type, like bright light (not in direct sunlight) also NOT too close to heating units / radiators and boilers, these make the tips of the leaf turn brown and dry, Keep all the leaves and stems dust free, by every few weeks use a damp sponge to wipe the foliage and stems, As for watering, when growing season starts, give enough water to wet the soil, (not flood) next watering, give a half strength liquid feed and there after full strength till about end September / October, then reduce watering and only JUST keep the soil from drying out.
Best way to find if you need to water is by sticking your finger down into the soil and is dry, water, if still damp leave for a few more days.
When you see Aeriel roots drop down from the upper stems, don't cut off but, try lead them down to the soil in the pot or saucer, these are required for the plant to take in humidity and air, it is a good idea to mist with hand warm temp water to the top and underside of foliage it helps remove dust too.
If you cut or break the plant leaf or stems, a white sap will ooze out, just wipe with a tissue or cloth and it will stop and heal OK, just try not get it on your skins as some folks are allergic to this.
When it is time to re-pot, you can either find a nice sturdy support or make a Moss pole/ Frame, the Moss frame / pole helps to give moisture to the Aeriel roots and they will grow into this as the mature, choose a bought compost that is easy to drain but not like, water just runs through it, I only re-pot mine when it gets to the stage that there is almost more root than soil in my pot, Remember you will need a large area for this plant as it grows, OR be prepared to cut it back from the top stem. IF you have to cut the top off, leave the cut stem to dry off for a day or two as you want the cut to heal before it goes into the soil or it might rot. plant the cutting and make sure there is a root or two in the soil to offer support, take up water and feed.
Last of all, should you get an odd leaf fall off or turns brown / yellow and is dying, then panic not, just try find the cause IF any and mist, feed as normal.