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The 2nd and 3rd warnings may both be tied to identification. The most likely cause in this model is that f1, f2 and f3 do not conform to a common factor model. The common factor "factor" has 3 variables exclusively dependent on it (plus 1 variable variable with shared dependency). To achieve identification, you will need at least 2 of those loadings (for f1, f2, f3) to be strong. Even though you have warning messages, parameter estimates are still available through lavaan:::summary(fit1). You will want to see that the three loadings are comparably large and not near 0. If you see something else, then maybe it is just a matter of starting values and you can sidestep the problem. But you could also look at the correlation matrix of f1, f2, f3 (using the cor() base function). The three variables must be substantially correlated, or else the factor model will not work.
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Karl Joreskog wrote a very keplful chapter that describes the differences between composite-based methods and factor-based methods. If you can grasp the proportionality constraints that are at the heart of factor-based methods, you will be able to intuit factor model results. If your 3 indicators do not have proportional correlations with the other variables in your model, then the factor model will perform poorly, even if the 3 are highly correlated among themselves.If you impose constraints just to make models over-identified, then all you are testing is the constraints. You could just as well use the t-values associated with the parameter estimates. But don't turn one model into multiple models and then compare predictors across models. Include all predictors in all models. Otherwise, the parameter estimates in the incomplete models will be biased due to the excluded variables.
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