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You can specify a higher output resolution than the archived resolution, but the resulting data will not contain any more information than the original, it has merely been interpolated[1] to a higher resolution. This makes the output look smoother, but does not increase the accuracy or the precision of the data. However, if you choose to interpolate to a coarser resolution than the archived resolution you should be aware that the data can be aliased, unless care was taken to avoid this.
does this still apply if interpolated to a new grid" is essentially yes but depends on how the interpolation is done and the relative grid resolutions. For example, clearly a nearest point interpolation to a much coarser grid would not give you a grid mean value representative of the new coarse grid, but averaging all the high-res grid points in the coarse grid box would be more representative of the larger scale average. When grids are similar resolution, then it just blurs the interpretation, but they can still effectively be treated as grid box averages, i.e. they are not point values.
For ERA-Interim atmospheric data the point interval on the native Gaussian grid is about 0.75 degrees. You can specify a custom grid using the CDS API or using the MARS client (if you have access to it).
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ERA5 HRES Ocean-Wave data are natively stored on the wave model’s reduced 0.36 degrees latitude/longitude grid.
Please be aware that quantities like temperature, i.e. can be treated as grid box averages but depends on how the interpolation is done and the relative grid resolutions. For example, a nearest point interpolation to a much coarser grid would not give a grid mean value representative of the new coarse grid, but averaging all the high-res grid points in the coarse grid box would be more representative of the larger scale average. When grids are similar resolution, then it just blurs the interpretation, but they can still effectively be treated as grid box averages, i.e. they are not point values.
[1] When data is interpolated, all continuous fields (e.g. precipitation, temperature) are interpolated by bilinear interpolation, and discrete fields (e.g. vegetation, precipitation type, soil type) and Wave 2D spectra are interpolated by nearest-neighbour. For more information about our grids and interpolations see in this presentation https://confluence.ecmwf.int/download/attachments/55122669/intro-interpolation-2016.pdf?api=v2
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